14 citations · 27 across the 13 of their papers we have counts for
4 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…
Derivatives of Theta Functions and a Problem of Lyubarskii and Nes
Lukas Liehr, Irina Shafkulovska, Mitchell A. Taylor
We characterize all lattices of rational density for which the Gabor system generated by the first Hermite function along is a frame for $L^2(\mathbb{R}…
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…
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…