## PD Peter Massopust, Ph.D.

PrivatdozentTechnische Universität München

Zentrum Mathematik - M15

Boltzmannstraße 3

85748 Garching Room: 02.08.040

Phone: +49 89 289 16826

eMail: massopustma.tum.de

## Research Interests

- Efficient Representations of Multidimensional Data via Frames, Wavelets, and Fractals
- Abstract and Applied Harmonic Analysis
- Functional Analysis
- Wavelets, Splines, and Frames
- Approximation and Interpolation Theory
- Fractal Analysis and Fractal Geometry

## Curriculum Vitae

## Recently Organized Conferences and Workshops

- Symposium on Higher-dimensional Splines: Variations on a Theme
^{}, ICNAAM 2014, September 22 - 28, 2014, Rhodes, Greece (with Patrick Van Fleet, University of St. Thomas, St. Paul, Minnesota, USA) - SampTA 2013
^{}, July 1 - 5, 2013 at the Jacobs University, Bremen, Germany (with Götz Pfander, Werner Henkel, Peter Oswald, Jacobs University Bremen, Peter Maaß, University of Bremen, Holger Rauhut, RWTH Aachen) - Summer School on New Trends and Directions in Harmonic Analysis, Fractional Operator Theory and Image Analysis, Sept. 17 - 22, 2012 in Inzell, Germany (with Brigitte Forster, Universität Passau)

## Recent Publications

**For a complete list of referred publications, technical reports, and other writings, please see my Curriculum Vitae.**

### Monographs

- P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets
^{}, Academic Press, 2nd ed., 426 + xix pp., August 2016.

### Text books

- P. Massopust, Interpolation and Approximation with Splines and Fractals
^{}, Oxford University Press, 336 pp., Jan. 2010. - B. Forster and P. Massopust, Eds., Contributors: O. Christensen, K. Gröchenig, D. Labate, P. Vandergheynst, G. Weiss, Y. Wiaux, Four Short Courses in Harmonic Analysis
^{}, Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag , approx. 250 pp., Nov. 2009.

### Edited books

- D. Larson, P. Massopust, M. Nguyen, M. Papadakis, Z. Nashed, and A. Zayed, eds.,
*Frames and Operator Theory in Analysis and Signal Processing,*Contemporary Mathematics, AMS Book Series, Vol. 451, 291 pp., 2008. - E. Grinberg, D. Larson, P. Massopust, P.E.T. Jorgensen, G. Olafsson, E.T. Quinto, and B. Rubin, eds.,
*Radon Transforms, Geometry, and Wavelets,*Contemporary Mathematics, AMS Book Series, 2008.

### Special Issues Edited

- Numerical Functional Analysis and Optimization: Special Issue on Operator Algebras and Representation Theory: Frames, Wavelets, and Fractals, Vol. 33, Issue 7--9, 2012 (with P. G. Casazza, Palle E. T. Jorgensen, Keri A. Kornelson, Gitta Kutyniok, David R. Larson, Gestur Olafsson, Judith A. Packer, Sergei D. Silvestrov and Qiyu Sun).
- Sampling Theory in Signal and Image Processing: Special Issue SampTA 2013, Proceedings of the International Conference on Sampling Theory and its Applications held at Jacobs-University Bremen, Germany, Vol. 13, Nos. 1--4, 2014 (with Götz Pfander and Holger Rauhut).

### Journal Articles

- P. Massopust, Fractal Interpolation: From Global to Local, to Nonstationary and Quaternionic, http://arxiv.org/abs/2108.13685, submitted 2021.
- S.R. Das, P. Massopust, and R. Ramakrishnan, B-splines on the Heisenberg group, http://arxiv.org/abs/2105.07707, submitted 2021.
- S. Verma and P. Massopust, Dimension Preserving Approximation, http://arXiv:2002.05061v2, submitted 2020.
- S.R. Das, P. Massopust, and R. Ramakrishnan, Twisted B-splines in the Complex Plane, Appl. Comput. Harmon. Anal. 56 (2022), 250--282.
- P. Massopust, Hypercomplex Iterated Function Systems, to appear in Current Trends in Analysis, its Applications and Computation. Proceedings of the 12th ISAAC Congress, Aveiro, Portugal, 2019, Cereijeras, P.; Reissig, M.; Sabadini, I.; Toft, J. (eds.), Birkh\"auser.
- P. Massopust, Splines and Fractional Differential Operators, International Journal of Wavelets, Multiresolution and Information Processing, DOI: 10.1142/S0219691320400056 (2020).
- P. Massopust, Interpolation and Sampling with Exponential Splines of Real Order, Results Math. 76 (2021), 76--121.
- N. Dyn, D. Levin, and P. Massopust, Attractors of Trees of Maps and of Sequences of Maps between Spaces with Applications to Subdivision, J. Fixed Point Theory Appl. 22, no. 1 (2020).
- L. Liehr and P. Massopust, On the Mathematical Validity of the Higuchi Method, Physcia D: Nonlinear Phenomena, 402 (2020), 28--37.
- P. Massopust, On Some Generalizations of B-Splines, Monografías Matemáticas García de Galdeano 42 (2019), 203 -- 217.
- J. Hogan and P. Massopust, Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling, Complex Analysis and Operator Theory 13 (2019), no. 7, 3373--3403.
- P. Massopust, Non-Stationary Fractal Interpolation, (invited contribution to Special Issue on "Fractals: Geometry, Analysis and Mathematical Physics"), Mathematics 2019, 7, 666, 1 - 14, DOI:10.3390/math7080666.
- M. Navascues and P. Massopust, Fractal Convolution: A New Operation between Functions, Fract. Calc. Appl. Anal., Vol. 22, No 3 (2019), pp. 619 - 643.
- P. Devaraj, P. Massopust, and S. Yugesh, Local average sampling and reconstruction with fundamental splines of fractional order, Numerical Functional Analysis and Optimization, 40(10) (2019), 1215 - 1229.
- P. Massopust, Local Fractal Interpolation on Unbounded Domains, Proc. Edinb. Math. Soc. (2) 61 (2018), no. 1, 151 – 167.
- J. Hogan and P. Massopust, Quaternionic B-Splines, J. Approx. Th. 224 (2017), 43 - 65.
- P. Massopust and P. Van Fleet, Fractional Cone and Hex Splines, Rocky Mountain Journal of Mathematics 47(5) (2017), 1655 - 1691.
- P. Massopust, B. Forster and O. Christensen, Fractional and Complex Pseudo-Splines and the Construction of Parseval Frames, Applied Mathematics and Computation 314 (2017), 12 - 24.
- A. Schindele, B. Forster, and P. Massopust, Multigrid Convergence for the MDCA-Curvature Estimator, Journal of Mathematical Imaging and Vision, Volume 57, Issue 3, (2017), 423 - 438.
- M. Storath, L. Demaret, and P. Massopust, Signal Analysis Based on Complex Wavelet Signs, Appl. Comput. Harmon. Anal. 42 (2017), no. 2, 199 – 223.
- M. Barnsley, M. Hegland, and P. Massopust, Self-referential Functions, submitted 2016.
- K. Hahn, P. Massopust and S. Prigarin, A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain, BMC Bioinformatics (2016), 17 - 87.
- P. Massopust, Local Fractal Functions in Besov and Triebel-Lizorkin Spaces, J. Math. Anal. Appl. 436 (2016), 393 - 407.
- P. Massopust and Ahmed I. Zayed, On the Invalidity of Fourier Series Expansions of Fractional Order, Fract. Calc. Appl. Anal., Vol. 18, No 6 (2015), 1507 - 1517.
- P. Massopust, Fractal Hypersurfaces, Wavelet Sets, and Affine Weyl Groups, Lecture Notes for Invited Presentations at the International Conference on Fractals, Wavelets and their Applications, Kerala, India, 2013.
- O. Christensen, B. Forster, and P. Massopust, Directional time frequency analysis via continuous frames, Bull. Aust.Math. Soc. 92 (2015), 268 - 281.
- P. Massopust, On local fractal functions in Banach spaces, AIP Conf. Proc. 1684 (2015), 64002-01 - 64002-04.
- M. F. Barnsley and P. Massopust, Bilinear Fractal Interpolation and Box Dimension, Journal of Approximation Theory, 192 (2015), 363 - 378.
- P. Massopust, Fractional Operators, Dirichlet Averages, and Splines, Applied and Numerical Harmonic Analysis: New Perspectives on Approximation and Sampling Theory (Festschrift in Honor of Paul Butzer's 85th Birthday) (2014), 399 - 422.
- P. Massopust, Exponential Splines of Complex Order, Contemporary Mathematics, Vol. 626 (2014), 87 - 106.
- P. Massopust, Local Fractal Functions and Function Spaces, Springer Proceedings in Mathematics & Statistics: Fractals, Wavelets, and their Applications, Vol. 92(2014), 245 - 270.
- M. F. Barnsley, M. Hegland, P. Massopust, Numerics and Fractals, Bulletin of the Institute of Mathematics, Academica Sinica (N.S.), Vol. 9(3)(2014), 389 - 430.
- M. Storath, L. Demaret and P. Massopust, Wavelet Signs: A New Tool for Signal Analysis, Proceedings of the 10th International Conference on Sampling Theory and Applications, EUROSIP, (2013), 45 - 48.
- B. Forster, R. Garunkstis, P. Massopust, and J. Steuding, Complex B-Splines and Hurwitz Zeta Functions, London Math. Soc. Journal of Computation and Mathematics 16(2013), 61 - 77.
- O. Christensen and P. Massopust, Exponential B-splines and the partition of unity property, Advances in Computational Mathematics 37(3)(2012), 301 - 318.
- P. Massopust, Splines of Complex Order: An Introduction, AIP Conference Proceedings, Vol. 1479 (2012), 991 - 994.
- B. Forster, P. Massopust and T. Übelacker, Periodic splines of complex order, Numerical Functional Analysis and Optimization, 33 (7 - 9)(2012), 989 - 1004.
- P. Massopust, Moments of Complex B-Splines, Commun. Math. Anal., Vol. 12, Number 2 (2012), 58 - 70.
- B. Forster and P. Massopust, Short Communication: Multivariate Interpolation with Fundamental Splines of Fractional Order, Proc. Appl. Math. Mech. Vol. 11 (2011), 857 - 858.
- B. Forster and P. Massopust, Splines of Complex order: Fourier, Filters, and Fractional Derivatives, Sampling Theory in Signal and Image Processing, Vol. 10, No. 1-2 (2011), 89 - 109.
- B. Forster and P. Massopust, Interpolation with fundamental splines of fractional order, Proceedings of SampTA 2011.
- S. Held, M. Storath, P. Massopust, and B. Forster, Steerable wavelet frames based on the Riesz transform, IEEE Transactions on Image Processing, Volume 19, Issue 3 (2010), 653 - 667.
- D. Larson, P. Massopust, and G. Olafsson, Three-way Tiling Sets in Two Dimensions, Acta Applicandae Mathematicae, 108 (2010), 529 - 546.
- P. Massopust and B. Forster, Multivariate Complex B-splines and Dirichlet Averages, J. Approx. Theory 162 (2010), 252 - 269.
- B. Forster and P. Massopust, Mathematical Aspects of Time Frequency Analysis, in: Four Short Courses in Harmonic Analysis, Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag (2009), 1 - 49.
- B. Forster and P. Massopust, Statistical Encounters with Complex B-Splines, Constr. Approx. 29 (2009), 325 - 344.
- P. Massopust, Double Dirichlet Averages and Complex B-Splines, Proceedings of Sampta 2009.
- B. Forster and P. Massopust, Multivariate Complex B-Splines, Dirichlet Averages and Difference Operators, Proceedings of Sampta 2009.
- B. Forster, P. Massopust, 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
- P. Massopust, P., D. Larson, Coxeter Groups and Wavelet Sets, Contemporary Mathematics, Vol. 451, 187 - 218, 2008
- B. Forster, P. Massopust, Multivariate Complex B-Splines, Proceedings of SPIE, Wavelets XII, Vol. 6701, 670109-1 – 670109-9, 2007
- P. Massopust, Multiwavelets: Some Approximation-Theoretic Properties, Sampling on the Interval, and Translation Invariance, Harmonic Analysis and p-Adic analysis, Eds. N. M. Chuong et al., World Scientific Publishing Co., 37 - 57, 2007
- P. Massopust, A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions, Advances in Deterministic and Stochastic Analysis, Eds. N. M. Chuong et al., World Scientific Publishing Co., 131 - 175, 2007

## Recent Grants and Sponsored Research

- BayFor (Bayerische Forschungsallianz) Grant for the initiation or immersion of international research collaborations: Multichannel Image and Signal Analysis: Phase and Geometry, Jan.--Dec. 2017 (with B. Forster and J. Hogan).
- BayFor (Bayerische Forschungsallianz) Grant for the initiation or immersion of international research collaborations: Efficient representations of multivariate signals, Jan.--Dec. 2015 (with B. Forster and O. Christensen).
- 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 Universität München, Office of the President, 2012--2014.
- VolkswagenStiftung: Summer School on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis, 2007.

## Editorialships

- Constructive Mathematical Analysis
- Fractal and Fractional
- Frontiers in Applied Mathematics and Statistics
- International Journal on Wavelets and Multiresolution Processing (IJWMIP)

## Recent and Forthcoming Invited Conference and Workshop Presentations

- International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), Plenary talk, IIT (BHU), Varanasi, India, Dec 2021.
- AMS Western Sectional Meeting, Special Session on "Fractal Geometry and Dynamical Systems," Albuquerque, USA, October 2021.
- 13th International Society for Analysis its Applications and Computation (ISAAC) Congress, Special Session on "Quaternionic and Clifford Analysis," Ghent, Belgium, August 2021.
- 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA12), Special Session on "Clifford Analysis," Hefei, China, August 2020.
- International Conference in "Functional analysis, Approximation Theory and Numerical Analysis," Special Session on "Operators in Function Spaces: convergence properties and applications," Matera, Italy, July 2020.
- Third Fractional Calculus Meeting, Plenary speaker, Universidad Zaragoza, Spain, September 2019.
- 12th International Society for Analysis its Applications and Computation (ISAAC) Congress, Special Session on "Quaternionic and Clifford Analysis," Aveiro, Portugal, July/August 2019.
- 9th International Congress on Applied and Industrial Mathematics (ICIAM), Minisymposium on "Fractals," Valencia, Spain, July 2019.
- 4th IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, March 2019.
- 15th International Conference on Mathematics and its Applications, Plenary speaker, Jaca, Spain, September, 2018.
- International Workshop on Operator Theory and Its Applications (IWOTA 2018), Special Session on "Spectral Theory and Differential Operators," Shanghai, China, July 2018.
- 11th International Conference on Clifford Algebras and Their Applications in Mathematical Physics (ICCA11), Minisymposium on "New Frontiers in Harmonic Analysis and Geometry over Non-Commutative Structures,", Ghent, Belgium, August 2017.
- 18th Annual Workshop on "Applications and Generalizations of Complex Analysis," Aveiro, Portugal, March 2017.
- 2nd IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, February 2017.
- Centre International de Rencontres Mathématiques (CIRM), "Multivariate Approximation and Interpolation with Applications," Marseille, France, September 2016.
- 4th Dolomites Workshop on "Constructive Approximation and Applications," Alba di Canazei, Italy, September 2016.
- 1st IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, February 2016.
- AMS Special Session on "Ergodic Theory and Dynamical Systems," AMS Annual Meetings, 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.
- Fifth International Conference on "Computational Harmonic Analysis," 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 de 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 (two presentations).
- International Workshop on Operator Theory and Its Applications, University of New South Wales, Sydney, Australia, July 2012.

## Current Collaborations

- IIT Madras
^{}, Chenai, India - Universidad de Zaragoza
^{}, Zaragoza, Spain - Tel-Aviv University
^{}, Tel-Aviv, Israel - Universidade de Aveiro
^{}, Aveiro, Portugal - University of Newcastle
^{}, Newcastle, Australia - Technical University Denmark (DTU)
^{}, Copenhagen, Denmark - Universität Passau
^{}, Passau, Germany - The Australian National University
^{}, Canberra, Australia - University of St. Thomas
^{}, St. Paul, USA - DePaul University
^{}, Chicago, USA - Vanderbilt University
^{}, Nashville, USA

## Short and Minicourses, Invited Lecture Series

- Fractal Geometry: Foundations to Frontiers, three-week long GIAN (Global Initiative of Academic Networks) lecture series, IIT Madras, India, August 2017, sponsored by the Government of India
- Splines and Fractals in Approximation and Interpolation Theory, two-week long GIAN (Global Initiative of Academic Networks) lecture series, IIT Madras, India, July 2016, sponsored by the Government of India.
- Wavelet Sets, Affine Weyl Groups, and Fractal Surfaces (three two-hour invited lectures), 18th European Intensive Course on Complex Analysis, its Applications and Generalizations, Universidade de Aveiro, Portugal, March 2013.
- Inverse Problems in Pipeline Inspection (one-hour invited lecture), AMS Short Course The Radon Transform and Applications to Inverse Problems, organized by G. Olafsson und T. Quinto, sponsored by the American Mathematical Society, Atlanta, Georgia, January 2005.
- Multiwavelets and their Applications (five-day mini-course), invited and sponsored by the Alleghany Section of the Mathematical Association of America, Meadville, Pennsylvania, Juni 1997.
- An Introduction to Fractal Functions and Fractal Surfaces and Their Connection to Wavelet Theory (three-day course), invited and sponsored by the Mathematical Association of America, San Francisco, California, January 1995).

## Teaching

### Winter Term 2021/2022

- Analysis 3
- Advanced Seminar: Mathematics for Data Science (offered every semester)

### Past Terms

- Differential and Integral Calculus (MSE) (Summer Term 2018, Summer Term 2020)
- Foundations of Mathematics (MSE) (Winter Term 2017/18, Winter Term 2019/20)
- Vector Analysis (Winter Term 2016/2017)
- Workshop: Iterated Function Systeme and Fractals (Summer Term 2016)
- Fourier and Laplace Transforms (Summer Term 2016, Summer Term 2017, Winter Term 2020/2021)
- Elements of the Theory of Distributions (Winter Term 2014/2015, Summer Term 2016, Summer Term 2019)
- Advanced Seminar: Models for Evolutionary Dynamics (with Prof. Dr. Ch. Kuttler and Dr. J. Perez-Valezquez) (Summer Term 2014)
- Higher Mathematics 3 for Electrical Engineering (Winter Term 2013/2014)
- Fractal Geometry (Winter Term 2010/2011, Summer Term 2013, Winter Term 2018/19)
- Complex Function Theory II (Winter Term 2009/2010, Winter Term 2012/2013, Winter Term 2015/2016, Winter Term 2017/18, Winter Term 2019/20)
- Lie Groups and Algebras (Summer Term 2012)
- Splines (Summer Term 2011)
- Advanced Seminar: Mathematical Methods for Image Processing - Inverse Problems (Summer Term 2011)
- Differential Forms (Winter Term 2007/2008, Summer Term 2010, Winter Term 2011/2012, Summer Term 2015, Winter Term 2016/2017, Summer Term 2018, Summer Term 2021)
- Advanced Seminar: Function Spaces (Winter Term 2009/2010)
- Meromorphic Functions and Riemannian Surfaces (Summer Term 2009)
- Proseminar: A Polynomial Approach to Linear Algebra (Winter Term 2008/2009)
- Topology (Summer Term 2008)
- Interpolation and Approximation with Splines and Fractals (Summer Term 2007)
- Proseminar: Complex Function Theory in the Plane and in Space (Summer Term 2007)
- Advanced Seminar: Image Analysis (Winter Term 2006/2007)

## Service to the University

- Academic counsellor for the study program Mathematics in Data Science.
- Aptitude assessment for the study program Mathematics in Data Science.