Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Faulhuber, Markus"'
Autor:
Faulhuber, Markus, Strohmer, Thomas
We introduce the new problems of quantum packing, quantum covering, and quantum paving. These problems arise naturally when considering an algebra of non-commutative operators that is deeply rooted in quantum physics as well as in Gabor analysis. Qua
Externí odkaz:
http://arxiv.org/abs/2408.08975
We study Gabor frames with Hermite window functions. Gr\"ochenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the ``safety region". For rectangular lattices and Hermite windows of order 4 an
Externí odkaz:
http://arxiv.org/abs/2403.10503
Proving the universal optimality of the hexagonal lattice is one of the big open challenges of nowadays mathematics. We show that the hexagonal lattice outperforms certain "natural" classes of periodic configurations. Also, we rule out the option tha
Externí odkaz:
http://arxiv.org/abs/2306.16266
We prove that among all 1-periodic configurations $\Gamma$ of points on the real line $\mathbb{R}$ the quantities $$ \min_{x \in \mathbb{R}} \sum_{\gamma \in \Gamma} e^{- \pi \alpha (x - \gamma)^2} \quad \text{and} \quad \max_{x \in \mathbb{R}} \sum_
Externí odkaz:
http://arxiv.org/abs/2305.01532
We study the spectral bounds of self-adjoint operators on the Hilbert space of square-integrable functions, arising from the representation theory of the Heisenberg group. Interestingly, starting either with the von Neumann lattice or the hexagonal l
Externí odkaz:
http://arxiv.org/abs/2209.04202
Autor:
Faulhuber, Markus, Shafkulovska, Irina
We study sharp frame bounds of Gabor systems over rectangular lattices for different windows and integer oversampling rate. In some cases we obtain optimality results for the square lattice, while in other cases the lattices optimizing the frame boun
Externí odkaz:
http://arxiv.org/abs/2204.02917
Autor:
Faulhuber, Markus
These lecture notes accompanied the course Time-Frequency Analysis given at the Faculty of Mathematics of the University of Vienna in the summer term 2021. The material is suitable for an advanced undergraduate course in mathematics or a mathematics
Externí odkaz:
http://arxiv.org/abs/2204.01596
We consider a two-dimensional analogue of Jacobi theta functions and prove that, among all lattices $\Lambda \subset \mathbb{R}^2$ with fixed density, the minimal value is maximized by the hexagonal lattice. This result can be interpreted as the dual
Externí odkaz:
http://arxiv.org/abs/2110.06008
Autor:
Bétermin, Laurent, Faulhuber, Markus
Publikováno v:
Journal d'Analyse Math\'ematique, 2023
We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H.~Montgomery. Minimal theta functions. \textit{Glasgow Mathematical Journal}, 30(1):75--85, 1988]. The studied theta func
Externí odkaz:
http://arxiv.org/abs/2007.15977
The goal of this work is to investigate the optimality of the $d$-dimensional rock-salt structure, i.e., the cubic lattice $V^{1/d}\mathbb{Z}^d$ of volume $V$ with an alternation of charges $\pm 1$ at lattice points, among periodic distribution of ch
Externí odkaz:
http://arxiv.org/abs/2004.04553