14 citations · 27 across the 13 of their papers we have counts for
14 papers
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}…
Gabor Frames of Totally Positive Functions: A Complete Characterization
Jaume de Dios Pont, Karlheinz Gröchenig, Lukas Liehr +2
We prove that the set of time-frequency shifts with a continuous, integrable totally positive function and lattice parameters $α…
Stability in unlimited sampling
José Luis Romero, Irina Shafkulovska
Folded sampling replaces clipping in analog-to-digital converters by reducing samples modulo a threshold, thereby avoiding saturation artifacts. We study the reconstruction of band…
A Characterization of Metaplectic Time-Frequency Representations
Karlheinz Gröchenig, Irina Shafkulovska
We characterize all time-frequency representations that satisfy a general covariance property: any weak*-continuous bilinear mapping that intertwines time-frequency shifts on the c…
More Uncertainty Principles for Metaplectic Time-Frequency Representations
Karlheinz Gröchenig, Irina Shafkulovska
We develop a method for the transfer of an uncertainty principle for the short-time Fourier transform or a Fourier pair to an uncertainty principle for a sesquilinear or quadratic…
Benedicks-type uncertainty principle for metaplectic time-frequency representations
Karlheinz Gröchenig, Irina Shafkulovska
Metaplectic Wigner distributions are joint time-frequency representations that are parametrized by a symplectic matrix and generalize the short-time Fourier transform and the Wigne…
On the frame property of Hermite functions and exploration of their frame sets
Markus Faulhuber, Irina Shafkulovska, Ilya Zlotnikov
We study Gabor frames with Hermite window functions. Gröchenig and Lyubarskii provided a sufficient density condition for their frame sets, which leads to what we call the "safety…
Sampling theorems with derivatives in shift-invariant spaces generated by periodic exponential B-splines
Karlheinz Gröchenig, Irina Shafkulovska
We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a…
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 metaplectic action on modulation spaces
Hartmut Führ, Irina Shafkulovska
We study the mapping properties of metaplectic operators on modulation spaces of the type . Our main r…
From completeness of discrete translates to phaseless sampling of the short-time Fourier transform
Philipp Grohs, Lukas Liehr, Irina Shafkulovska
We study the uniqueness problem in short-time Fourier transform phase retrieval by exploring a connection to the completeness problem of discrete translates. Specifically, we prove…
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…
Gabor frame bound optimizations
Markus Faulhuber, Irina Shafkulovska
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 squar…