Preprints
- M. Faulhuber. The polarization problem for the honeycomb structure, September 2025.
https://doi.org/10.48550/arXiv.2509.24687 - L. Betermin, M. Faulhuber, S. Steinerberger. A variational principle for Gaussian lattice sums, October 2021.
https://arxiv.org/abs/2110.06008
Journal articles
- M. Faulhuber. Gabor systems with Hermite functions of order N and oversampling greater than N+1 which are not frames. Sampling Theory, Signal Processing, and Data Science, 23:22, September 2025.
https://doi.org/10.1007/s43670-025-00112-5
https://arxiv.org/abs/2502.09510 - M. Faulhuber, I. Shafkulovska, I. Zlotnikov. On the frame property of Hermite functions and exploration of their frame sets. Journal of Fourier Analysis and Applications, 31:21, April 2025.
https://doi.org/10.1007/s00041-025-10153-y
https://arxiv.org/abs/2403.10503 - M. Faulhuber, A. Gumber, I. Shafkulovska. The AGM of Gauss, Ramanujan’s corresponding theory, and spectral bounds of self-adjoint operators. Monatshefte für Mathematik, 206(3):551-582, March 2025.
https://doi.org/10.1007/s00605-024-02051-0
https://arxiv.org/abs/2209.04202 - M. Faulhuber, I. Shafkulovska, I. Zlotnikov. A note on energy minimization in dimension 2. Proceedings of the American Mathematical Society Series B, 11(2024):664-679, December 2024.
https://doi.org/10.1090/bproc/247
https://arxiv.org/abs/2306.16266 - M. Faulhuber, S. Steinerberger. Maximal polarization for periodic configurations on the real line. International Mathematics Research Notices, 2024(9):7914-7943, May 2024.
https://doi.org/10.1093/imrn/rnae003
https://arxiv.org/abs/2305.01532 - M. Faulhuber, I. Shafkulovska. Gabor frame bound optimizations. Applied and Computational Harmonic Analysis 67:101574, November 2023.
https://doi.org/10.1016/j.acha.2023.101574
https://arxiv.org/abs/2204.02917 - L. Betermin, M. Faulhuber. Maximal Theta Functions – Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies. Journal d’Analyse Mathématique, 149(1):307-341, April 2023.
https://doi.org/10.1007/s11854-022-0254-z
https://arxiv.org/abs/2007.15977 - M. Faulhuber. Some Curious Results Related to a Conjecture of Strohmer and Beaver. Analysis and Applications, 19(5):845-873, September 2021.
https://doi.org/10.1142/S0219530520500177
https://arxiv.org/abs/1901.00356 - L. Betermin, M. Faulhuber, H. Knüpfer. On the optimality of the rock-salt structure among lattices with charge distributions. Mathematical Models and Methods in Applied Sciences, 31(2):293-325, February 2021.
https://doi.org/10.1142/S021820252150007X
https://arxiv.org/abs/2004.04553 - M. Faulhuber. Extremal Determinants of Laplace-Beltrami Operators for Rectangular Tori. Mathematische Zeitschrift 297(1-2):175-195, February 2021.
https://doi.org/10.1007/s00209-020-02507-7
https://arxiv.org/abs/1709.06006 - M. Faulhuber. An Application of Hypergeometric Functions to Heat Kernels on Rectangular and Hexagonal Tori and a “Weltkonstante” – Or – How Ramanujan Split Temperatures. The Ramanujan Journal 54(1):1-27, January 2021.
https://doi.org/10.1007/s11139-019-00224-2
https://arxiv.org/abs/1901.01218 - M. Faulhuber. On the Parity under Metaplectic Operators and an Extension of a Result of Lyubarskii and Nes. Results in Mathematics, 75(8). March 2020.
https://doi.org/10.1007/s00025-019-1134-4
https://arxiv.org/abs/1901.01220 - M. Faulhuber, M. de Gosson, D. Rottensteiner. Gaussian Distributions and Phase Space Weyl-Heisenberg Frames. Applied and Computational Harmonic Analysis, 48(1):374-394, January 2020.
https://doi.org/10.1016/j.acha.2018.06.001
https://arxiv.org/abs/1708.01551 - M. Faulhuber, S. Steinerberger. An Extremal Property of the Hexagonal Lattice. Journal of Statistical Physics, 177(2):285-298. October 2019.
https://doi.org/10.1007/s10955-019-02368-3
https://arxiv.org/abs/1903.06856 - M. Faulhuber. A Short Note on the Frame Set of Odd Functions. Bulletin of the Australian Mathematical Society, 98(3):481-493. December 2018.
https://doi.org/10.1017/S0004972718000746
https://arxiv.org/abs/1710.00753 - M. Faulhuber. Minimal Frame Operator Norms via Minimal Theta Functions. Journal of Fourier Analysis and Applications, 24(2):545-559. April 2018.
https://doi.org/10.1007/s00041-017-9526-x
https://arxiv.org/abs/1608.01168 - M. Faulhuber, S. Steinerberger. Optimal Gabor frame bounds for separable lattices and estimates for Jacobi theta functions. Journal of Mathematical Analysis and Applications, 445(1):407–422. January 2017.
https://doi.org/10.1016/j.jmaa.2016.07.074
https://arxiv.org/abs/1601.02972 - M. Faulhuber. Gabor frame sets of invariance: a Hamiltonian approach to Gabor frame deformations. Journal of Pseudo-Differential-Operators and Applications, 7(2):213-235. June 2016.
https://doi.org/10.1007/s11868-016-0146-z
https://arxiv.org/abs/1509.04603
Conference proceedings
- M. Faulhuber. Operator-isomorphism pairs and Zak transform methods for the study of Gabor systems. Proceedings of the 15th International Conference on Sampling Theory and Applications (SampTA), Vienna Austria, August 2025.
https://doi-org.uaccess.univie.ac.at/10.1109/SampTA64769.2025.11133554
https://arxiv.org/abs/2502.08358 - M. Faulhuber. On the frame set property of Hermite functions. Applied Harmonic Analysis and Data Science, Oberwolfach, April 2024.
https://doi.org/10.14760/OWR-2024-21 - M. Faulhuber. Gaussian lattice sums. Applied Harmonic Analysis and Data Science, Oberwolfach workshop, December 2021.
https://doi.org/10.14760/OWR-2021-55 - M. Faulhuber. The Strohmer and Beaver Conjecture for Gaussian Gabor Systems – A Deep Mathematical Problem (?). Proceedings of the 13th International Conference on Sampling Theory and Applications (SampTA), Bordeaux France, July 2019.
https://doi.org/10.1109/SampTA45681.2019.9030963
https://arxiv.org/abs/1905.05051 - M. Dörfler, M. Faulhuber. Multi-Window Weaving Frames. Proceedings of the 12th International Conference on Sampling Theory and Applications, July 2017.
https://doi.org/10.1109/SAMPTA.2017.8024450
https://arxiv.org/abs/1705.04166 - L. Wiedemann, T. Haftner, B. Pobatschnig, M. Faulhuber, M. Reichel. Qualitätsbetrachtung der Wavelet- und RMS Analyse in Abhängigkeit der Aufnahmefrequenz von EMG Signalen. In UMIT – Lecture Notes in Biomedical Computer Science and Mechatronic., C. Baumgartner, W. Mayr (eds.), Volume 4, pp 19-20, September 2014.
ISBN: 978-3-9503191-3-2
Book Chapters
- M. Faulhuber, T. Strohmer. Quantum paving: When sphere packings meet Gabor frames. In Sampling, Frames, and Harmonic Analysis: A Mathematical Celebration of Akram Aldroubi’s 65th Birthday, C. Cabrelli, C. E. Heil, U. Molter, A. M. Powell (editors). Applied and Numerical Harmonic Analysis. (to appear)
https://arxiv.org/abs/2408.08975
Lecture notes
- Time-Frequency Analysis (Lecture Notes)
https://arxiv.org/abs/2204.01596
Doctoral thesis
M. Faulhuber. Extremal Bounds of Gaussian Gabor Frames and Properties of Jacobi’s Theta Functions. Doctoral thesis, University of Vienna, December 2016.
Habilitation thesis
M. Faulhuber. Discrete extremal problems in low dimensions. Habilitation thesis, University of Vienna, October 2023.