34 citations · 111 across the 25 of their papers we have counts for
8 papers · 1 filter
Asymptotic safety regions for Gabor frames generated by Hermite functions
Markus Faulhuber, Irina Shafkulovska, Ilya Zlotnikov
The aim of this paper is to establish new regions in the frame sets of Hermite functions . A classical result of Gröchenig and Lyubarskii shows that the Gabor system $\mathcal…
On a fundamental barrier of the Wirtinger criterion for Gabor systems with odd functions
Markus Faulhuber
We show that the Wirtinger criterion cannot be used to investigate the frame set conjecture for the first Hermite function. More generally, for odd functions, it cannot determine r…
The polarization problem for the honeycomb structure
Markus Faulhuber
We study the polarization problem in dimension 2 for the honeycomb structure and compare it to the maximal polarization lattice, the hexagonal lattice. As expected, the hexagonal l…
A note on energy minimization in dimension 2
Markus Faulhuber, Irina Shafkulovska, Ilia Zlotnikov
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…
Maximal polarization for periodic configurations on the real line
Markus Faulhuber, Stefan Steinerberger
We prove that among all 1-periodic configurations of points on the real line the quantities $$ \min_{x \in \mathbb{R}} \sum_{γ\in Γ} e^{- πα(x - γ)^2} \quad \text{…
The AGM of Gauss, Ramanujan's corresponding theory, and spectral bounds of self-adjoint operators
Markus Faulhuber, Anupam Gumber, Irina Shafkulovska
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. Interest…
A variational principle for Gaussian lattice sums
Laurent Bétermin, Markus Faulhuber, Stefan Steinerberger
We consider a two-dimensional analog of Jacobi theta functions and prove that, among all lattices with fixed density, the minimal value is maximized by the…
An Application of Hypergeometric Functions to Heat Kernels on Rectangular and Hexagonal Tori and a "Weltkonstante" -- Or -- How Ramanujan Split Temperatures
Markus Faulhuber
In this work we investigate the heat kernel of the Laplace--Beltrami operator on a rectangular torus and the according temperature distribution. We compute the minimum and the maxi…