Home Page of PD Peter Massopust, Ph.D.

AFFILIATION:

Privatdozent

Centre of Mathematics

Lehrstuhl für Mathematische Modellierung – M6

Technische Universität München

Boltzmannstrasse 3

85747 Garching b. München

Tel. +49 (0)89 289 16811

E-Mail: massopust@ma.tum.de

Germany

and

Scientist

Helmholtz Zentrum München

Ingolstädter Landstrasse 1

85764 Neuherberg

Tel. +49 (0)89 3187 2436

E-Mail: peter.massopust@helmholtz-muenchen.de

Germany

EDUCATION:

Habilitation Technische Universität München, Germany, 2011

Habilitationsschrift: The Multiscale Structure of Fractal
Functions and Wavelets

Ph.D. Georgia Institute of Technology, U.S.A., 1986

Thesis Title: Space Curves Generated by Iterated Function Systems

Thesis Advisor: Michael F. Barnsley

M.S. Mathematics Georgia Institute of Technology, U.S.A. 1985

M.S. Physics Georgia Institute of Technology, U.S.A. 1981

B.S. Mathematics Ludwig-Maximilians Universität München, Germany, 1980

(Vordiplom)

B.S. Physics Ludwig-Maximilians Universität München, Germany, 1980

(Vordiplom)

MAIN AREAS OF INTEREST:

- Abstract and Applied Harmonic Analysis
- Wavelets, Splines, and Frames
- Approximation and Interpolation Theory
- Fractal Analysis and Geometry

GRANTS AND SPONSORED RESEARCH:

- DFG (German Research Foundation) Grant: Splines of Complex
Order, Fractional Operators, and Applications in Signal and
Image Processing, 2014--2016.

- Start-Up Grant for Cooperation between EuroTech Universities, Technische Universit\"at M\"unchen, 2012.
- VolkswagenStiftung: Summer School on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis, 2007.
- Research Grant: Function Spaces and Numerical Approximations with Wavelets, Sandia National Laboratories, 1998--1999.
- Co-Principal Investigator: An Investigation of Wavelet Bases for Grid-Based Multi-Scale Simulation, Sandia National Laboratories Internal Grant (LDRD), 1997--1998.
- Co-Principal Investigator: Wavelets Based on Several Scaling Functions and Related Applications, National Science Foundation Grant, DMS, 1995--1998.
- Principal Investigator: Summer Faculty Research Program, AFOSR, 1995.
- Principal Investigator: Summer Faculty Research Program, AFOSR, 1994.
- Principal Investigator: Summer Faculty Research Program, AFOSR, 1993.
- NATO Travel Grant: Advanced Research Workshop: Shape in Picture, The Netherlands, 1992.
- Faculty Research Grant: State University of West Georgia, 1989--1990.

SCHOLARSHIPS AND FELLOWSHIPS

- Fulbright Scholarship (1980-1981)
- Visiting Fellowship, Institute of Mathematical Sciences, Australian National University, Canberra, Australia (February 2008)
- Visiting Fellowship, Institute of Mathematical Sciences, Australian National University, Canberra, Australia (July/August 2012)
- Visiting Fellowship, Institute of Mathematical Sciences,
Australian National University, Canberra, Australia (May/June
2013)

EDITORIALSHIPS

- Journal of Mathematics (Hindawi Publishing Corporation)
- International Journal of Advances in Mathematics
- International Journal on Wavelets and Multiresolution
Processing (IJWMIP)

RESEARCH EXPERIENCE / COLLABORATIONS:

- Universidade do Aveiro, Portugal

- Yamaguchi University, Japan
- Vilnius University, Lithuania

- University of Würzburg, Germany

- University of Passau, Germany
- Technical University of Denmark (DTU), Denmark
- The Australian National University, Australia
- University of St. Thomas, U.S.A.

- Louisiana State University, U.S.A.
- Texas A & M University, U.S.A.
- Rice University, U.S.A.
- Vanderbilt University, U.S.A.
- Georgia Institute of Technology, U.S.A.
- Sandia National Laboratories, U.S.A.
- Tuboscope Pipeline Services, U.S.A.
- Arnold Engineering and Development Center (AEDC), U.S.A.

PUBLICATIONS:

Books

Authored:

- Interpolation and Approximation with Splines and Fractals, 336 pp., Oxford University Press, Jan. 2010
- Four Short Courses in Harmonic Analysis, 249 pp., Birkhäuser Verlag, Nov. 2009 (with B. Forster; Contributors: O. Christensen, K. Gröchenig, D. Labate, P. Vandergheynst, G. Weiss, Y. Wiaux)
- Fractal Functions, Fractal Surfaces, and Wavelets, Research monograph, 384 pp., Academic Press 1995.

- Frames and Operator Theory in Analysis and Signal Processing,Contemporary Mathematics, Vol. 451, 291 pp., 2008 (with D. Larson, M. Nguyen, M. Papadakis, Z. Nashed, and A. Zayed)
- Radon Transforms, Geometry, and Wavelets, Contemporary Mathematics, Vol. 464, 265 pp., 2008 (with E. Grinberg, D. Larson, P. E. T. Jorgensen, G. Ólafsson, T. Quinto, and B. Rubin)

- The Capacity for a Class of Fractal Functions, Commun. Math. Phys., 105 (1986), 455 – 460 (with D.P. Hardin)
- Dynamical Systems, Fractal Functions, and Dimension, Topology Proceedings, 12 (1987), 93 – 110.
- Fractal Modeling of Biological Structures, Ann. NY Acad. Sci., 504(1987), 179 – 194 (with M.F. Barnsley, H. Strickland, and A. D.Sloan)
- Fractal Peano Curves, J. of Geometry, 34 (1989), 127 – 138.
- Hidden Variable Fractal Interpolation Functions, SIAM J. Math. Anal., 20(5) (1989), 1218 – 1248(with M. F. Barnsley, J. Elton, and D. P. Hardin)
- Fractal Surfaces, J. Math. Anal. and Appl., 151(1) (1990), 275 – 290.
- Vector-Valued Fractal Interpolation Functions and their Box Dimension, Aequationes Mathematicae, 42(1991), 1 – 22.
- The Exact Hausdorff Dimension for a Class of Fractal Functions, J. Math. Anal. and Appl., 168(1992), 171 – 183 (with S. Gibert).
- Multiresolution Analyses Based on Fractal Functions, J. Approx. Theory, 71(1) (1992), 104 – 120 (with D. Hardin and B. Kessler)
- Fractal Interpolation Functions from R
^{n}to R^{m}and their Projections,Zeitschrift für Analysis u. i. Anwend., 12 (1993),535 – 548(with D. P. Hardin) - Smooth Interpolating Curves and Surfaces Generated by Iterated Function Systems, Zeitschrift für Analysis u. i. Anwend., 12(1993), 201 – 210.
- Characterization of all Solutions to a Perturbed Laplace Equation II, Rocky Mountain J. Math., 24, No. 2(1994), 549 – 562 (with J. Kelingos)
- Fractal Surfaces, Multiresolution Analyses, and Wavelet Transforms, NATO ASI Series F, Vol. 106(1994), 275 – 290 (with J. S. Geronimo and D. P. Hardin)
- An Application of Coxeter Groups to the Construction of
Wavelet Bases in R
^{n }, Lecture Notes in Pure and Applied Mathematics: Fourier Analysis - Analytic and Geometric Theory, Vol. 157 (1994), 187 – 196 (with J. S. Geronimo and D. P. Hardin) - Fractal Functions and Wavelets Expansions Based on Several Scaling Functions, J. Approx. Th., 78(3)(1994), 373 – 401 (with J. S. Geronimo and D. P. Hardin)
- A Characterization of Solutions to a Radially Perturbed Laplace Equation in the unit n-ball, J. Math. Anal. and Appl., 199 (1996), 728 – 747 (with J. Kelingos).
- Construction of Orthogonal Wavelets Using Fractal Interpolation Functions, SIAM J. Math. Anal., 27(4) (1996), 1158 – 1192 (with G. Donovan, J. Geronimo, and D. Hardin)
- On the Support Properties of Scaling Vectors, Applied and Computational Harmonic Analysis, 3(1996), 229 – 238 (with D. Ruch and P. Van Fleet)
- Fractal Functions and Multiwavelets, Proceedings of Fractals in Engineering 97, Arcachon, France, June 1997.
- Fractal Functions and their Applications, Chaos, Solitons, and Fractals, 8(2) (1997), 171 – 190.
- Generalized Multiresolution Schemes, J. Math. Anal. and Applications, 221 (1998), 574 – 594.
- A Multiwavelet Based on Piecewise C
^{1}Fractal Functions and Related Applications to Differential Equations, Bol. Soc. Mat. Méxicana, (3), Vol 4 (1998), 249 – 283. - Divergence-Free Multiwavelets, Approximation Theory IX (C. K. Chui and L. L. Schumaker, eds.), 2 (1998), 161 – 168 (with J. Lakey and C. Pereyra)
- Translation Invariant Multiwavelet Transforms, Technical Report CML TR 98-06, Computational Mathematics Laboratory, Rice University, 1998 (with Kathrin Berkner)
- On angularly perturbed Laplace equations in the unit ball
of R
^{n+2 }and their distributional boundary values, in Analysis of Divergence, (W. O. Bray and C. V. Stanojevic, eds.) (1999),

359 – 378. - Hierarchical rule based classification of MFL signals obtained from natural gas pipeline inspection, IEEE-INNS-ENNS international joint conference on neural networks, Vol. 5, pp. 71 – 76, 2000 (mit J. Y. Lee, M. Afzal, S. Udpa, und L. Udpa)
- Multisensor Fusion for 3-D Characterization Using Wavelet Basis Neural Network, Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, Eds, Vol. 20A, American Institute of Physics, pp. 679 – 694, 2001 (mit J. Lim, S. Udpa, L. Udpa, und M. Afzal)
- Fractal Functions and Wavelets: Examples of Multiscale Theory, in Abstract and Applied Analysis, Proceedings of the International Conference, Hanoi, Vietnam, 13 – 27 August, 2002, (N. M. Chuong, L. Nirenberg, W. Tutschke, eds.), World Scientific Press, Singapore, 2004.
- Fractal Functions, Splines, and Besov and Triebel-Lizorkin Spaces, in Fractals in Engineering: New trends and applications (J. Lévy-Véhel, E. Lutton, eds.), 21 – 32, Springer Verlag, London, 2005.
- Inverse problems in Pipeline Engineering, in The Radon Transform, Inverse Problems, and Tomography, (G. Ólafsson, E. T. Quinto, Eds.), AMS Proceedings on Symposia in Applied Mathematics 63, 93 – 128, Providence, Rhode Island, 2006.
- A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions, Advances in Deterministic and Stochastic Analysis, (N. M. Chuong, P. G. Ciarlet, P. Lax, D. Mumford and D. H. Phong, Eds.), 131 – 175, World Scientific Publishing Co., 2007.
- Multiwavelets: Some Approximation-Theoretic Properties, Sampling on the Interval, and Translation Invariance, Harmonic, Wavelet and p-Adic Analysis, (N. M. Chuong et al. Eds.), 37 – 57, World Scientific Publishing Co., 2007.
- Multivariate Complex B-Splines, Proceedings of SPIE, Wavelets XII, Vol. 6701, 670109-1 – 670109-9, 2007 (with B. Forster)
- Coxeter Groups and Wavelets Sets, Contemporary Mathematics, Vol. 451 (2008), 187 – 218 (with D. Larson)
- Some Remarks about the Connection between Fractional Divided Differences, Fractional B-Splines, and the Hermite-Genocchi Formula, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 6, No. 2, 2008, 279 – 290 (with. B. Forster)
- Statistical Encounters with Complex B-Splines, Constr. Approx. 29 (2009), 325 – 344 (with B. Forster)
- Three-way Tiling Sets in Two Dimensions, Acta Applicandae Mathematicae 108(3) (2009), 529 – 546 (with D. Larson and G. Ólafsson)
- Multivariate Complex B-splines and Dirichlet Averages, J. Approx. Th. 162 (2010), 252 – 269 (with B. Forster)
- Multivariate Complex B-Splines, Dirichlet Averages, and Difference Operators, Proceedings of SampTA, 4 pp., 2009 (with B. Forster)
- Double Dirichlet Averages and Complex B-Splines, Proceedings of SampTA, 4 pp., 2009.
- Isotropic Wavelet Frames Based on the Riesz Transform, IEEE Transactions on Image Processing, Vol. 19 (3) (2010), 653 – 667 (with B. Forster, S. Held, and M. Storath)
- Interpolation with Fundamental Splines of Fractional Order, Proceedings of SampTA 2011 (with B. Forster)
- Splines of Complex Order: Fourier, Filters, and Fractional Derivatives, Sampling Theory in Signal and Image Analysis, Vol. 10, No. 1 – 2 (2011), 89 – 109 (with B. Forster)
- Moments of complex B-splines, Commun. Math. Anal., Vol. 12, No. 2 (2012), 58 – 70.
- Short Communication: Multivariate Interpolation with Fundamental Splines of Fractional Order, Proc. Appl. Math. Mech., 11 (2011), 857--858 (with B. Forster)
- Periodic splines of complex order, Numerical Functional Analysis and Optimization 33(7 – 9) (2012), 989 – 1004 (with B. Forster and T. Übelacker)
- Splines of complex order: An introduction, AIP Conference Proceedings, Vol. 1479 (2012), 991--994.
- Exponential B-Splines and the Partition of Unity Property, Adv. Comput. Math. 37(3)(2012), 301 - 318 (with O. Christensen)
- Complex B-Splines and Hurwitz Zeta Functions, London Math.
Soc. Journal of Computation and Mathematics 16(2013), 61--77
(with B. Forster, Ramūnas Garunkštis, and Jörn Steuding)

- Wavelet Signs: A New Tool for Signal Analysis, Proceedings of the 10th International Conference on Sampling Theory and Applications, EUROSIP, (2013), 45--48 (with M. Storath and L. Demaret).
- Fractional Operators, Dirichlet Averages, and Splines, invited paper, Festschrift honoring Paul Butzer, 2014, in press.
- Exponential Splines of Complex Order, Contemporary Mathematics, 2014, in press.
- Numerics and fractals, to appear in Bulletin of the Institute of Mathematics, Academica Sinica (N.S.) (with M. F. Barnsley and M. Hegland)
- Local fractal functions and function fpaces, to appear in Springer Proceedings in Mathematics & Statistics.
- Signal analysis based on complex wavelet signs, http://arxiv.org/abs/1208.4578, 2013 (with M. Storath and L. Demaret).
- Bilinear fractal interpolation and box dimension, submitted to Constructive Approximation, http://arxiv.org/abs/1209.3139, 2014 (with Michael F. Barnsley).
- Fractal hypersurfaces, wavelet sets, and affine Weyl groups, invited conference proceedings paper, International Conference \& Workshop on Fractals and Wavelets, http://arxiv.org/abs/1309.0241, 2013.
- Directional time frequency analysis via continuous frames, http://arxiv.org/abs/1402.3682, 2014 (with O. Christensen and B. Forster)
- Local fractal functions in Besov and Triebel-Lizorkin spaces,
http://arxiv.org/abs/1408.6355, 2014.

Industrial and Technical Reports

Some reports in the following collection contain novel but unpublished material due to proprietary constraints.

- A study of Wavelet-Galerkin methods for numerical solutions of differential equations using multigrid relaxation methods, Technical Report, AFOSR Faculty Summer Research Program, July 1993, 14pp.
- A wavelet-multigrid approach to solving partial differential equations based on fractal functions, Technical Report, AFOSR Faculty Summer Research Program, August 1994, 17pp.
- Multiresolution schemes for solving conservation laws, Technical Report, AFOSR Faculty Summer Research Program, August 1995, 19 pp.
- Scaling vectors and multiwavelets in numerical differential equations – Some approximation – theoretic and numerical issues, Sandia Technical Report, SAND97-2133, UC-405, September 1997, 51pp.
- Local stable splittings and wavelet packets, Technical Report for Sandia National Laboratories, May 1998, 15pp.
- Nonlinear approximation, wavelet packets, and interpolation, Technical Report for Sandia National Laboratories, July 1998, 20pp.
- On magnetic fields generated by Cartesian, cylindrical, spherical, and parabolic defects. Part I: Analytical solutions, Tuboscope Technical Report TR-1999-01, 1999. [First systematic and analytic derivation of solutions for the magnetic forward problem, 52 pp.]
- Circumferential sensor evaluation, Tuboscope Technical Report TR-1999-02, 1999. [Proves that the radial component of the magnetic field can be used to simulate the circumferential component, 18 pp.]
- Fourier and Wavelet analysis of defects, Tuboscope Technical Report TR-2000-01, 2000. [Feasibility study to detect boundaries in defects using wavelets, 13pp]
- MFL signal enhancement via wavelet-based denoising, Tuboscope Technical Report TR-2000-05, 2000 (with A. Belanger). [Removal of white noise using wavelets, 32pp]
- Axial and circumferential local curvature calculations for strain estimation and their error analyses, Tuboscope Technical Report TR-2000-06, 2000. [First systematic study and error analysis for industry-wide used procedure to estimate strain, 30pp]
- Two-dimensional wavelet-based denoising, Tuboscope Technical Report TR-2001-02, 2001. [Feasibility study to remove white noise using tensor-product wavelets, 21 pp.]
- Knot removal and knot insertion for two-dimensional mechanical damage data, Tuboscope Technical Report TR-2001-03, 2001. [Novel algorithms to enhance mechanical data, 17 pp.]
- Computation of the strain tensor field for mechanical damage data, Tuboscope Technical Report TR-2001-04, 2001. [First analytic derivation of the strain field based on industry standards, 14 pp.]
- Modified exact solutions, Tuboscope Technical Report TR-2002-02, 2002. [Second order improvement of exact solutions, 14 pp.]
- Pipeline integrity assessment algorithms: Statistical foundations, Tuboscope Technical Report TR-2002-04, 2002. [First comprehensive and detailed analysis of probability of detection and error analysis based on rigorous mathematical statistics for Tuboscope inspection tools, 15 pp.]
- A short note on hysteresis and odd harmonics, Tuboscope Technical Report TR-2002-05, 2002. [Exact derivation of hysteresis curves using a Preisach model and relation to nonlinear harmonic excitations, 5 pp.]
- Compression of ILI data using wavelet packets, Tuboscope Technical Report TR-2002-07, 2002. [Feasibility study to compress inline inspection data, 42 pp.]
- A short note on ILI data correction due to pipe deformation, Tuboscope Technical Report TR-2002-08, 2002. [Derivation of data correction for deformed pipe, 2 pp.]
- Mathematical analysis of ILI data, Tuboscope Technical Report TR-2003-02, 2003. [First rigorous analysis of Tuboscope’s tool data using mathematical statistics, 12 pp.]
- Signal enhancement via B-Spline representations, Tuboscope Technical Report TR-2003-07, 2003 (with A. Belanger). [Feasibility study to enhance inspection data using B-spline techniques, 11 pp.]
- Reconstruction of clipped MFL signals via B-spline approximation and Hermite interpolation, Tuboscope Technical Report TR-2004-04, 2004. [Algorithm to reconstruct clipped signals, 16 pp.]
- Removal of seamless pipe noise via curvelets, Tuboscope Technical Report, TR-2006-01, 2006. [Algorithm for the effective removal of seamless pipe noise, 22 pp.

- Fractals and their geometry, The Georgia Mathematics Newsletter, Issue No. 13, Fall 1989. [6 pp.]
- An introduction to fractal functions and fractal surfaces and their connection to wavelet theory, Lecture notes for a three-day minicourse sponsored by the MAA, 1995. [56 pp.]
- Multiwavelets and their applications, Lectures notes for a week-long minicourse sponsored by the MAA, 1997. [51 pp.]
- The benefits of combining technologies for in-line inspection, 3R International, (42) Heft 7, (2003) (with M. Slaughter and C. Torres)[Description of the advantage of combined technologies, some of which are based on my mathematical contributions, in pipeline inspection, 4 pp.]

DISCOVERY DISCLOSURE:

GHM (Geronimo-Hardin-Massopust) Scaling Vector and DGHM (Donovan-Geronimo-Hardin-Massopust) Multiwavelet, Georgia Tech Research Institute, Atlanta, U.S.A., 1995. (with G. Donovan, D. Hardin and J. Geronimo)

SHORT AND MINICOURSES PRESENTED:

- Inverse Problems in Pipeline Inspection, invited presentation for the AMS Short Course entitled The Radon Transform and Applications To Inverse Problems (organized by G. Ólafsson and T. Quinto and sponsored by the AMS, Atlanta, Georgia, January 2005)
- Multiwavelets and their Applications (invited and sponsored by the Alleghany Section of the MAA, Meadville, Pennsylvania, June 1997).
- An Introduction to Fractal Functions and Fractal Surfaces and Their Connection to Wavelet Theory (invited and sponsored by the MAA, San Francisco, California, January 1995).

TEACHING EXPERIENCE:

Lectures

Germany:

- Higher Mathematics 3 for Electrical Engineers (Winter Semester
2913/2014)

- Lie Groups and Algebras (Summer Semester 2012)
- Splines (Summer Semester 2011)
- Fractal Geometry (Winter Semester 2010/2011, Summer Semester 2013)
- Function Theory II (Winter Semester 2009/2010, Winter Semester 2012/2013)
- Meromorphic Functions and Riemann Surfaces (Summer Semester 2009)
- Topology (Summer Semester 2008)
- Differential Forms (Winter Semester 2007/2008, Summer Semester 2010, Wintersemester 2011/2012)
- Interpolation and Approximation with Splines and Fractals (Summer Semester 2007)

- Finite and Discrete Mathematics
- Calculus I - V
- Ordinary Differential Equations
- Real Analysis
- Partial Differential Equations
- Probability Theory
- Complex Analysis
- Fractal Geometry
- Numerical Analysis
- Numerical Methods for Ordinary and Partial Differential Equations
- Mathematical Physics
- Physics I+II

- Hauptseminar: Models of Evolutionary Dynamics (SS 2014)

- Hauptseminar: Mathematical Methods in Imaging - Inverse Problems (SS 2011)
- Hauptseminar: Function Spaces (WS 2009/2010)
- Proseminar: A Polynomial Approach to Linear Algebra (WS 2007/2008)
- Proseminar: Function Theory in the Plane and in Space (SS 2007)
- Hauptseminar: Image Analysis (WS 2006/2007)
- Oberseminar: Wavelets and Function Spaces (Vanderbilt University, 1992)

- Stefan Held, Ph.D. Thesis: Hypercomplex Wavelets for the Analysis of Image Data (2012)
- Andreas Schindele, Mathematics Master Thesis: Curvature Profile in Black and White Images (2012)
- Kristof Schröder, Mathematics Master Thesis: Reconstruction of Band-Pass Signals from Zero Sets (2012)
- Andreas Hangauer, Mathematics Diploma Thesis: Construction of Coiflets Associated with Multiwavelets (2009)
- Susanne Schmalkalt, Mathematics Diploma Thesis: Directional Filtering in Images Demonstrated in the Case of Nerve Fibres (2009)
- Florian Drechsler, Mathematics Diploma Thesis: Wavelet-Sets and Reflection Groups (2007)

- Srijanani Anurag Prasad, Indian Institute of Technology Kanpur (India), May 2011
- Elena Babace, University of Skopje (Macedonia), April 2009
- Robert Scealy, The Australian National University (Australia), October 2008
- Arya Kumar Bedabrata Chand, Indian Institute of Technology Kanpur (India), May 2005

MEMBERSHIPS AND OTHER SCHOLARLY ACTIVITIES:

- Member of Phi Mu Epsilon (National Honorary Mathematics Fraternity)
- Member of Sigma Pi Sigma (Physics Honor Society)
- Invited member of IAG (International Association of Geodesy) Special Study Group IAG-SSG 4.195, Fractal Geometry in Geodesy
- Refereed for more than 60 international journals
- Reviewer for Mathematical Reviews
- Reviewer for Zentralblatt Mathematik
- National Science Foundation Panel Judge

CONFERENCE AND SCIENTIFIC COMMITTEES:

- International Conference on Fractals and Wavelets, Rajagiri
School of Engineering & Technology, Kakkanad Cochin, Kerala,
India, November 2013.

- Sampling Theory and its Applications (SampTA) 2013, Jacobs-University Bremen, Germany, July 2013.
- Summer School on New Trends and Directions in Harmonic Analysis, Fractional Operator Theory, and Image Analysis, Inzell, Germany, September 2012
- Minisymposium on Phase Information in Signals and Images, Joint Annual Meeting of the Deutsche Mathematiker-Vereinigung (DMV) and the Gesellschaft für Didaktik und Mathematik (GDM), Munich, Germany, March 2010.
- Summer School on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis, Inzell, Germany, September 2007.
- Special Session on Frames and Wavelets in Harmonic Analysis, Geometry and Applications, Annual Meeting of the AMS in New Orleans, Louisiana, January 2007.
- Special Session on Frames and Operator Theory in Analysis and Signal Processing, Annual Meeting of the AMS in San Antonio, Texas, January 2006.
- Second International Conference on Applied and Abstract Analysis, Qui Nhon, Vietnam, June 2005.
- First International Summer School on Harmonic, Wavelet and p-adic Analysis, Qui Nhon, Vietnam, June 2005.
- Invited Special Session on Design and Applications of Multidimensional Wavelets and MRAs, Wavelets XI, SPIE International Symposium on Optical Science and Technology, SPIE 50th Annual Meeting, San Diego, California, July/August 2005.
- Special Session on Designing Frames and Wavelets: From Theory to Digitization, Sixth Joint Meeting of the America Mathematical Society and the Sociedad Matemática Méxicana, Houston, Texas, May 2004.
- International Conference on Abstract and Applied Analysis 2002, A satellite conference of the International Congress of Mathematicians (ICM) 2002, Hanoi, Vietnam, August 2002.
- Special Session on (Multi)wavelets and Numerical PDEs, Western Sectional Meeting of the AMS, University of New Mexico, Albuquerque, New Mexico, November 1997.
- International Conference on Multiwavelets: Theory and Applications, Sam Houston State University, Huntsville, Texas, March 1997.

INVITED PRESENTATIONS AT NATIONAL AND INTERNATIONAL CONFERENCES AND WORKSHOPS:

- AMS Special Session "Ergodic Theory and Dynamical Systems,"
AMS Annual Meeting, San Antonio, U.S.A., January 2015.

- International Conference on New Directions in Fractal Geometry, The Australian National University, Canberry, Australia, November 2014.
- International Conference Numerical Analysis and Applied
Mathematics 2014, Minisymposium on Fractal Analysis and Harmonic
Analysis, Rhodes, Greece, September 2014.

- International Conference on Computational Harmonic Analyis,
Nashville, Tennessee, May 2014.

- International Conference on Fractals and Wavelets, Rajagiri
School of Engineering & Technology, Kakkanad Cochin, Kerala,
India, November 2013.

- CIMPA 2013, New Trends in Harmonic Analysis, Mar del Plata, Argentina, August 2013.
- AMS Special Session on "Harmonic Analysis of Frames, Wavelets,
and Tilings," University of Colorado, Colorado, April 2013.

- Gesellschaft für Angewandte Mathematik und Mechanik (GAMM 2013), Mathematical Image and Signal Processing, Novi Sad, Serbia, March 2013.
- European Intensive Course on Complex Analysis, its Generalizations and Applications, Universidade do Aveiro, Portugal, March 2013 (three two-hour lectures).
- International Conference on Advances on Fractals and Related Topics, Chinese University of Hong Kong, China, December 2012.
- International Conference Numerical Analysis and Applied Mathematics 2012, Kos, Greece, September 2012.
- International Workshop on Operator Theory and Applications, University of New South Wales, Sydney, Australia, July 2012.
- International Conference on Sampling Theory and Applications (SampTA 2011), Singapore, May 2011.
- Gesellschaft für Angewandte Mathematik und Mechanik (GAMM 2011), Mathematical Image Processing, Graz, Austria, April 2011.
- Workshop on Operator Algebras and Representation Theory: Frames, Wavelets and Fractals, Banff International Research Station, Canada, October 2010.
- International Conference on Wavelets and Applications, St. Petersburg, Russia, June 2009.
- Poster Presentation, SampTA 2009, Marseille, France, May 2009.
- Seminar-Präsentation, Texas A & M University, Texas, April 2009.
- Research Mini-Workshop Coxeter Groups and Wavelet Sets, Texas A & M University, Texas, March 30 – April 3, 2009.
- Computational Analysis Seminar, Vanderbilt University, Tennessee, March 2009.
- NeuWave Imaging Workshop, Technische Universität München, April 2008.
- Wavelets XII, SPIE Conference, San Diego, U.S.A., August 2007.
- Mini-Workshop on Geometric Measure Theorretic Approaches to Potentials on Fractals and Manifolds, Oberwolfach Research Institute, Oberwolfach, Germany, April 2007.
- 47. Workshop on Approximationstheorie, Universität Erlangen – Nürnberg, February 2007.
- Workshop on Operator Methods in Fractal Analysis, Wavelets, and Dynamical Systems, Banff International Research Station, Canada, December 2006.
- IMA/MCIM Industrial Problems Seminar, Mathematical Problems associated with a Class of Nondestructive Evaluations, IMA, Minneapolis, Minnesota, March 2006.
- Workshop on Harmonic Analysis and Fractal Geometry, Louisiana State University, Baton Rouge, Louisiana, February 2006.
- Workshop on New Mathematics and Algorithms for 3-D Image Analysis, Institute of Mathematics and its Applications (IMA), University of Minnesota, Minneapolis, Minnesota, January 2006.
- International Conference on Fractals in Engineering V, Tours, France, June 2005.
- First International Summer School on Harmonic, Wavelet, and p-adic Analysis, Qui Nhon University, Qui Nhon, Vietnam (two one-hour lectures), June 2005.
- Second International Conference on Abstract and Applied Analysis, ICAAA 2005, Qui Nhon, Vietnam (plenary lecture), June 2005.
- Special Session on The Radon Transform and Inverse Problems, Annual Meeting of the AMS, Atlanta, Georgia, January 2005.
- Workshop on Functional and Harmonic Analyses of Wavelets and Frames, Institute of Mathematical Sciences, National University of Singapore, Singapore, August 2004
- Workshop on New Mathematics and Algorithms for 3D Image Analysis, Louisiana State University, Baton Rouge, Louisiana, September, 2003.
- Special Session on Wavelets, Frames, and Tomography, Southeastern Sectional Meeting of the AMS, Baton Rouge, Louisiana, March 2003.
- International Conference on Abstract and Applied Analysis, a satellite conference of the International Congress of Mathematics, Hanoi, Vietnam, August 2002.
- Special Session on (Multi)wavelets and Numerical PDEs, Western Regional Meeting of the AMS, Albuquerque, New Mexico, November 1997.
- International Conference on Fractals in Engineering III, Arcachon, France, June 1997.
- Seventh International Workshop in Analysis and its Applications, University of Maine, Orono, Maine, June 1997.
- Minisymposium on Wavelets and their Applications, SIAM Annual Meeting, Kansas City, Missouri, July 1996.
- Special Session on Numerical Solutions of Nonlinear Partial Differential Equations, Second Meeting of the AMS and the Sociedad Matemática Méxicana, Guanajuato, México, November 1995.
- Special Session on Wavelets and Applications, International Conference on Applied Science and Computations, Eastern Illinois University, Charleston, Illinois, October 1995.
- Third US National Congress of Computational Mechanics, Dallas, Texas, June 1995.
- Special Session on New Trends in Generalized Functions, Southeastern Regional Meeting of the AMS, Orlando, Florida, March 1995.
- 31st Annual Symposium of the Society of Engineering Science, Texas A & M University, College Station, Texas, October 1994.
- NATO Advanced Research Workshop, Shape in Picture, Driebergen, The Netherlands, September 1992.
- Sixth International Workshop on Analysis and it Applications, University of Maine, Orono, Maine, June 1992.

INVITED COLLOQUIA AND SEMINAR TALKS:

- University of Passau, Germany.
- Imperial College London, United Kingdom.
- Jacobs-University Bremen, Germany
- Technical University of Denmark (DTU), Lyngby, Denmark
- The Australian National University, Canberra, Australia
(several occasions)

- Technische Universität München, Munich, Germany
- Helmholtz Zentrum München, Insitute for Biomathematics and
Biometry, Munich, Germany

- University of North Texas, Denton, Texas, USA
- Texas A & M University, College Station, Texas, USA (several occasions)
- University of Houston, Houston, Texas, USA (several occasions)
- Tuboscope Pipeline Service, Houston, Texas, USA (several occasions)
- Iowa State University, Ames, Iowa, USA
- University of St. Thomas, St. Paul, Minnesota, USA (several occasions)
- Rice University, Houston, Texas, USA
- Center of Approximation Theory, Texas A & M University, College Station, Texas, USA (several occasions)
- Vanderbilt University, Nashville, Tennessee, USA (several occasions)
- New Mexico Institute of Mining and Technology, Socorro, New Mexico, USA
- Sandia National Laboratories, Albuquerque, New Mexico, USA
- Sam Houston State University, Huntsville, Texas, USA (several occasions)
- University of Central Florida, Orlando, Florida, USA
- Arnold Engineering and Development Center (AEDC), Tullahoma, Tennessee, USA
- Bradley University, Peoria, Illinois, USA
- University of Tennessee Space Institute, Tullahoma, Tennessee, USA
- University of Louisville, Louisville, Kentucky, USA
- Georgia Institute of Technology, Atlanta, Georgia, USA (several occasions)
- State University of West Georgia, Carrollton, Georgia, USA
- LaGrange College, LaGrange, Georgia, USA
- North Harris College, Houston, Texas, USA (several occasions)