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Technical University of Munich
Technical University of Munich

Peter Massopust

Technical University of Munich
School of Computation, Information and Technology
Department of Mathematics
Boltzmannstr. 3
85748 Garching b. München

Office: MI 02.08.040 (find my room)
Phone number: +49 89 289 16826
Privatdozent
Email: massopust@ma.tum.de
 

Academic background

Education:

  • Habilitation 2011 (Technical University of Munich), Germany;
  • Ph.D. Applied Mathematics 1986 (Georgia Institute of Technology, USA);
  • MS Mathematics 1985 (Georgia Institute of Technology, USA);
  • MS Physics 1981 (Georgia Institute of Technology, USA).

if you want to see the extended version, click on CURRICULUM VITAE.

Research interests

  • Wavelets and Frames
  • Harmonic and Functional Analysis
  • Fractal Geometry and Fractal Interpolation Theory
  • Splines and Approximation Theory.

2023

  • DAS, Santi; RAMAKRİSHNAN, Radha; MASSOPUST, Peter: Systems of left translates and oblique duals on the Heisenberg group. Constructive Mathematical Analysis, 2023, 222-236 more… Full text ( DOI )
  • Kumar, D.; Chand, A. K. B.; Massopust, P. R.: Multivariate Zipper Fractal Functions. Numerical Functional Analysis and Optimization, 2023, 1-32 more… Full text ( DOI )
  • Massopust, Peter: Fractal hypersurfaces, affine Weyl groups, and wavelet sets. The Journal of Analysis, 2023 more… Full text ( DOI )

2022

  • Das, S.R.; Massopust, P.; Radha, R.: Twisted B-splines in the complex plane. Applied and Computational Harmonic Analysis 56, 2022, 250-282 more… Full text ( DOI )
  • Kumar, Deependra; Chand, Arya K. B.; Massopust, Peter R.: Approximation by Quantum Meyer-König-Zeller Fractal Functions. Fractal and Fractional 6 (12), 2022, 704 more… Full text ( DOI )
  • Massopust, Peter R.: Fractal interpolation over nonlinear partitions. Chaos, Solitons & Fractals 162, 2022, 112503 more… Full text ( DOI )
  • Peter Massopust: Fractal interpolation: From global to local, to non-stationary and quaternionic. In: S. Banerjee and A. Gowrisankar (Ed.): Frontiers of Fractal Analysis: Recent Advances and Challenges. CRS Press, 2022 more…
  • Verma, S.; Massopust, P. R.: Dimension preserving approximation. Aequationes mathematicae 96 (6), 2022, 1233-1247 more… Full text ( DOI )

2021

  • Massopust, Peter: Interpolation and Sampling with Exponential Splines of Real Order. Results in Mathematics 76 (3), 2021 more… Full text ( DOI )

2020

  • Liehr, Lukas; Massopust, Peter: On the mathematical validity of the Higuchi method. Physica D: Nonlinear Phenomena 402, 2020, 132265 more… Full text ( DOI )
  • Massopust, Peter: Splines and fractional differential operators. International Journal of Wavelets, Multiresolution and Information Processing 20 (03), 2020 more… Full text ( DOI )

2019

  • Devaraj, P.; Massopust, Peter; Yugesh, S.: Local Average Sampling and Reconstruction with Fundamental Splines of Fractional Order. Numerical Functional Analysis and Optimization 40 (10), 2019, 1215-1229 more… Full text ( DOI )
  • Dyn, Nira; Levin, David; Massopust, Peter: Attractors of trees of maps and of sequences of maps between spaces with applications to subdivision. Journal of Fixed Point Theory and Applications 22 (1), 2019 more… Full text ( DOI )
  • Hogan, Jeffrey A.; Massopust, Peter R.: Quaternionic Fundamental Cardinal Splines: Interpolation and Sampling. Complex Analysis and Operator Theory 13 (7), 2019, 3373-3403 more… Full text ( DOI )
  • Massopust, Peter: Non-Stationary Fractal Interpolation. Mathematics 7 (8), 2019, 666 more… Full text ( DOI )
  • Massopust, Peter: Non-Stationary Fractal Interpolation. Mathematics 7 (8), 2019, 666 more… Full text ( DOI )
  • Navascués, María A.; Massopust, Peter R.: Fractal Convolution: A New Operation Between Functions. Fractional Calculus and Applied Analysis 22 (3), 2019, 619-643 more… Full text ( DOI )
  • Peter Massopust: On some generalizations of B-splines. Monografías Matemáticas García de Galdeano (42), 2019, 203--217 more…

2018

  • Massopust, Peter R.: Local Fractal Interpolation on Unbounded Domains. Proceedings of the Edinburgh Mathematical Society 61 (1), 2018, 151-167 more… Full text ( DOI )

2017

  • Hogan, Jeffrey A.; Massopust, Peter: Quaternionic B-splines. Journal of Approximation Theory 224, 2017, 43-65 more… Full text ( DOI )
  • Massopust, Peter R.; Fleet, Patrick J. Van: Fractional cone and hex splines. Rocky Mountain Journal of Mathematics 47 (5), 2017 more… Full text ( DOI )
  • Massopust, Peter; Forster, Brigitte; Christensen, Ole: Fractional and complex pseudo-splines and the construction of Parseval frames. Applied Mathematics and Computation 314, 2017, 12-24 more… Full text ( DOI )
  • Storath, Martin; Demaret, Laurent; Massopust, Peter: Signal analysis based on complex wavelet signs. Applied and Computational Harmonic Analysis 42 (2), 2017, 199-223 more… Full text ( DOI )

2016

  • Hahn, Klaus; Massopust, Peter R.; Prigarin, Sergei: A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain. BMC Bioinformatics 17 (1), 2016 more… Full text ( DOI )
  • Massopust, Peter R.: On local fractal functions in Besov and Triebel–Lizorkin spaces. Journal of Mathematical Analysis and Applications 436 (1), 2016, 393-407 more… Full text ( DOI )
  • Schindele, Andreas; Massopust, Peter; Forster, Brigitte: Multigrid Convergence for the MDCA Curvature Estimator. Journal of Mathematical Imaging and Vision 57 (3), 2016, 423-438 more… Full text ( DOI )

2015

  • Barnsley, Michael F.; Massopust, Peter R.: Bilinear fractal interpolation and box dimension. Journal of Approximation Theory 192, 2015, 362-378 more… Full text ( DOI )
  • CHRISTENSEN, OLE; FORSTER, BRIGITTE; MASSOPUST, PETER: DIRECTIONAL TIME–FREQUENCY ANALYSIS VIA CONTINUOUS FRAMES. Bulletin of the Australian Mathematical Society 92 (2), 2015, 268-281 more… Full text ( DOI )
  • Massopust, Peter R.; Zayed, Ahmed I.: On the Invalidity of Fourier Series Expansions of Fractional Order. Fractional Calculus and Applied Analysis 18 (6), 2015, 1507-1517 more… Full text ( DOI )

2014

2013

  • Forster, B.; Garunkštis, R.; Massopust, P.; Steuding, J.: Complex B-splines and Hurwitz zeta functions. LMS Journal of Computation and Mathematics 16, 2013, 61-77 more… Full text ( DOI )

2012

  • Forster, Brigitte; Massopust, Peter; Übelacker, Thomas: Periodic Splines of Complex Order. Numerical Functional Analysis and Optimization 33 (7-9), 2012, 989-1004 more… Full text ( DOI )
  • P.R. Massopust: Moments of complex B-splines. Commun. Math. Anal. (12(2)), 2012, 58--70 more…

2011

  • B. Forster and P.R. Massopust: Splines of complex order: Fourier, filter, and fractional derivatives. Sampling Theory in Signal and Image Analysis (10(1--2)), 2011, 89--109 more…
  • B. Forster and P.R. Massopust: Short Communication: Multivariate Interpolation with Fundamental Splines of Fractional Order. Proc. Appl. Math. Mech. (11), 2011, 857--858 more…
  • Christensen, Ole; Massopust, Peter: Exponential B-splines and the partition of unity property. Advances in Computational Mathematics 37 (3), 2011, 301-318 more… Full text ( DOI )

2010

  • B. Forster, S. Held, M. Storath and P.R. Massopust: Isotropic wavelet frames based on the Riesz transform. IEEE Transactions on Image Processing 19(3), 2010, 653--667 more…
  • Held, S.; Storath, M.; Massopust, P.; Forster, B.: Steerable Wavelet Frames Based on the Riesz Transform. IEEE Transactions on Image Processing 19 (3), 2010, 653-667 more… Full text ( DOI )
  • Massopust, Peter; Forster, Brigitte: Multivariate complex B-splines and Dirichlet averages. Journal of Approximation Theory 162 (2), 2010, 252-269 more… Full text ( DOI )
  • Massopust, Peter; Forster, Brigitte: Multivariate complex B-splines and Dirichlet averages. Journal of Approximation Theory 162 (2), 2010, 252-269 more… Full text ( DOI )

2009

  • Larson, David R.; Massopust, Peter; Ólafsson, Gestur: Three-Way Tiling Sets in Two Dimensions. Acta Applicandae Mathematicae 108 (3), 2009, 529-546 more… Full text ( DOI )

2008

  • B. Forster and P.R. 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 6(2), 2008, 279--290 more…
  • D. Larson and P.R. Massopust: Coxeter groups and wavelets sets. Contemp. Math. 451, 2008, 187--218 more…
  • Forster, Brigitte; Massopust, Peter: Statistical Encounters with Complex B-Splines. Constructive Approximation 29 (3), 2008, 325-344 more… Full text ( DOI )

1998

  • P.R. Massopust: Generalized multiresolution schemesJ. Math. Anal. and Applications. J. Math. Anal. and Appl. (221), 1998, 574--594 more…
  • P.R. Massopust: A multiwavelet based on piecewise $C^1$-- fractal functions and related applications to differential equations. Bol. Soc. Mat. Méxicana (3(4)), 1998, 249--283 more…

1997

  • P.R. Massopust: Fractal functions and their applications. Chaos, Solitons, and Fractals (8(2)), 1997, 171--190 more…

1996

  • D. Ruch, P. Van Fleet and P.R. Massopust: On the support properties of scaling vectors. Appl. Comp. Harmon. Anal. (3), 1996, 229--238 more…
  • G. Donovan, J. Geronimo, D. Hardin and P.R. Massopust: Construction of orthogonal wavelets using fractal interpolation functions. SIAM J. Math. Anal. (27(4)), 1996, 1158--1192 more…
  • J. Kelingos and P.R. Massopust: A Characterization of solutions to a radially perturbed Laplace equation in the unit $n$-ball. J. Math. Anal. and Appl. (199), 1996, 728--747 more…

1994

  • J. Kelingos and P.R. Massopust: Characterization of all solutions to a perturbed Laplace equation II. Rocky Mountain J. Math. (24(2)), 1994, 549--562 more…
  • J. S. Geronimo, D. P. Hardin and P.R. Massopust: Fractal surfaces, multiresolution analyses, and wavelet transforms. NATO ASI Series F (106), 1994, 275--290 more…
  • J. S. Geronimo, D. P. Hardin and P.R. Massopust: Fractal functions and wavelets expansions based on several scaling functions. J. Approx. Th (78(3)), 1994, 373--401 more…
  • J. S. Geronimo, D. P. Hardin and P.R. Massopust: An application of Coxeter groups to the construction of wavelet bases in $\mathbb{R}^n$. Lecture Notes in Pure and Applied Mathematics: Fourier Analysis - Analytic and Geometric Theory, 1994, 187--196 more…

1993

  • D. P. Hardin and P.R. Massopust: Fractal interpolation functions from $\mathbb{R}^n$ to $\mathbb{R}^m$ and their projections. Zeitschrift für Analysis u. i. Anwend. (12), 1993, 535--548 more…
  • P.R. Massopust: Smooth interpolating curves and surfaces generated by iterated function systems. Zeitschrift für Analysis u. i. Anwend. (12), 1993, 201--210 more…

1992

  • S. Gibert and P.R. Massopust: The exact Hausdorff dimension for a class of fractal functions. J. Math. Anal. and Appl. (168), 1992, 171--183 more…

1991

  • P.R. Massopust: Vector-valued fractal interpolation functions and their box dimension. Aequationes Mathematicae (42), 1991, 1--22 more…

1990

  • P.R. Massopust: Fractal surfaces. J. Math. Anal. and Appl. (151(1)), 1990, 275--290 more…

1989

  • M.F. Barnsley, J. Elton, D. Hardin and P.R. Massopust: Hidden variable fractal interpolation functions. SIAM J. Math. Anal (20(5)), 1989, 1218--1248 more…
  • P.R. Massopust: Fractal Peano curves. J. of Geometry (34), 1989, 127--138 more…

1987

  • M.F. Barnsley, P.R. Massopust, H. Strickland and A.D. Sloan: Fractal modeling of biological structures. Ann. NY Acad. Sci (504), 1987, 179--194 more…
  • P.R. Massopust: Dynamical systems, fractal functions and dimension. Topology Proceedings (12), 1987, 93--110 more…

1986

  • D.P. Hardin and P. R. Massopust: The capacity for a class of fractal functions. Commun. Math. Phys. (105), 1986, 455--460 more…

2023

  • Kumar, D.; Chand, A. K. B.; Massopust, P. R.: Multivariate Bernstein $$\alpha $$-Fractal Functions. In: Lecture Notes in Networks and Systems. Springer Nature Singapore, 2023 more… Full text ( DOI )
  • Massopust, Peter R.: Clifford-Valued Fractal Interpolation. In: Springer Proceedings in Mathematics & Statistics. Springer Nature Singapore, 2023 more… Full text ( DOI )

2021

  • Massopust, Peter: Hypercomplex Iterated Function Systems. In: Trends in Mathematics. Springer International Publishing, 2021 more… Full text ( DOI )

2015

  • Massopust, Peter: On local fractal functions in banach spaces. AIP Conference Proceedings, AIP Publishing LLC, 2015 more… Full text ( DOI )

2013

  • M. Storath, L. Demaret and P.R. Massopust: Wavelet Signs: A New Tool for Signal Analysis. Proceedings of the 10th International Conference on Sampling Theory and Applications, EUROSIP, 2013, 45--48 more…

2012

2011

  • B. Forster and P.R. Massopust: Interpolation with fundamental splines of fractional order. Proceedings of SampTA 2011, 2011, 1--4 more…

2009

  • B. Forster and P.R. Massopust: Multivariate complex B-splines, Dirichlet averages and difference operators. Proceedings of SampTA 2009, 2009, 1--4 more…
  • P.R. Massopust: Double Dirichlet averages and complex B-splines. Proceedings of SampTA 2009, 2009, 1--4 more…

2007

  • P.R. Massopust: A class of solutions to Maxwell's equations in matter and associated special functions. Advances in Deterministic and Stochastic Analysis, 2007, 131--175 more…
  • P.R. Massopust: Multiwavelets: Some approximation-theoretic properties, sampling on the interval, and translation invariance. Harmonic, Wavelet and $p$-Adic Analysis, 2007, 37--57 more…

2006

  • P.R. Massopust: Inverse problems in pipeline engineering. The Radon Transform, Inverse Problems, and Tomography, AMS Proceedings on Symposia in Applied Mathematics 63, 2006, 93--128 more…

2005

  • P.R. Massopust: Fractal functions, splines, and Besov and Triebel-Lizorkin spaces. Fractals in Engineering: New trends and applications, 2005, 21--32 more…

2004

  • P.R. Massopust: Fractal functions and wavelets: Examples of multiscale theory. Abstract and Applied Analysis, 2004, 225--248 more…

2001

  • J. Lim, S. Udpa, L. Udpa, M. Afzal and P.R. Massopust: Multisensor fusion for 3-D characterization using wavelet basis neural networks. Review of Progress in Quantitative Nondestructive Evaluation, Vol. 20A, American Institute of Physics, 2001, 679--695 more…

2000

  • J. Y. Lee, M. Afzal, S. Udpa, L. Udpa and P.R. Massopust: Hierarchical rule based classification of MFL signals obtained from natural gas pipeline inspection. IEEE-INNS-ENNS International Joint Conference on Neural Networks, 2000, 71--76 more…

1999

  • P.R. Massopust: On angularly perturbed Laplace equations in the unit ball of $\mathbb{R}^{n+2}$ and their distributional boundary values. Analysis of Divergence, 1999, 359--378 more…

1997

  • P.R. Massopust: Fractal functions and multiwavelets. Proceedings of Fractals in Engineering: New Trends in Theory and Applications, 1997, 97 more…

2016

  • P.R: Massopust: Fractal Functions, Fractal Surfaces, and Wavelets. Academic Press (2. edn.), 2016 more…

2010

  • P.R. Massopust: Interpolation and Approximation with Splines and Fractals. Oxford University Press, 2010 more…

2009

  • B. Forster and P.R. Massopust: Four Short Courses in Harmonic Analysis. Birkhäuser Verlag, 2009 more…

2008

  • E. Grinberg, D. Larson, P.E.T. Jorgensen, P.R: Massopust, G. Óafsson, E.T. Quinto, and B. Rubin: Radon transforms, geometry, and wavelets. Contemporary Mathematics, AMS Book Series, Vol. 464, 2008 more…
  • With D. Larson, P.R. Massopust, M. Nguyen, M. Papadakis, Z. Nashed, and A. Zayed: Frames and Operator Theory in Analysis and Signal Processing. Contemporary Mathematics, AMS Book Series, Vol. 451, 2008 more…

2022

  • Peter Massopust: Fractal Interpolation - From Global to Local, to Non-Stationary and Quaternionic – Chapter 2. In: Frontiers of Fractal Analysis. CRC Press, 2022 more…

2021

  • Massopust, Peter: Hypercomplex Iterated Function Systems. In: Trends in Mathematics. Springer International Publishing, 2021 more… Full text ( DOI )

2014

  • Massopust, Peter: Fractional Operators, Dirichlet Averages, and Splines. In: New Perspectives on Approximation and Sampling Theory. Springer International Publishing, 2014 more… Full text ( DOI )
  • Massopust, Peter R.: Local Fractal Functions and Function Spaces. In: Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2014 more… Full text ( DOI )

2009

  • B. Forster and P.R. Massopust: Mathematical Aspects of Time Frequency Analysis. In: B. Forster and P.R. Massopust (Ed.): Four Short Courses in Harmonic Analysis. Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag, 2009, 1--49 more…

1998

  • J. Lakey, C. Pereyra and P.R. Massopust: Divergence-free multiwavelets. In: C. K. Chui and L. L. Schumaker (Ed.): Approximation Theory IX. Academic Press, 1998, 161--168 more…

  • EuroTech Visiting Researcher Programme: Focus Artificial Intelligence (Development of Novel Mathematical Algorithms), TUM -- DTU, 2023.
  • Bayerische Forschungsallianz (BayFor): Multichannel Image and Signal Analysis: Phase and Geometry, Jan.--Dec. 2017.
  • Bayerische Forschungsallianz (BayFor): Efficient Representations of Multidimensional Signals, Jan.--Dec. 2015.
  • 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, 2012--2014.
  • 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.

  • 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)
  • GIAN (Global Initiative for Academic Network) Award, Republic of India (July 2016)
  • GIAN (Global Initiative for Academic Network) Award, Republic of India (July/August 2017)

Editorialships

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)

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