Preprints
- M. Faulhuber, I. Shafkulovska, I. Zlotnikov. A note on energy minimization in dimension 2, June 2023.
https://arxiv.org/abs/2306.16266 - M. Faulhuber, S. Steinerberger. Maximal polarization for periodic configurations on the real line, May 2023.
https://arxiv.org/abs/2305.01532 - M. Faulhuber, A. Gumber, I. Shafkulovska. The AGM of Gauss, Ramanujan’s corresponding theory, and spectral bounds of self-adjoint operators, September 2022.
https://arxiv.org/abs/2209.04202 - 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, 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, February 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. 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
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.