11 citations · 41 across the 16 of their papers we have counts for
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Bohr sets for multiplier algebras of complete Pick spaces
Ole Fredrik Brevig, Kristian Seip, Ilya Zlotnikov
We reexamine F. Wiener's classical proof that the Bohr radius of is . We replace by the multiplier algebras of complete Pick spaces and describe the Bohr…
Periodic Non-uniqueness Sets for Shift-invariant Spaces and Parity-Based Obstructions to the Frame Property for Gabor Systems
Alexander Ulanovskii, Ilya Zlotnikov
The goal of this note is twofold. First, we provide explicit examples of periodic (though not necessarily lattice) sets that give rise to Gabor systems failing to form frames. Our…
Extreme and exposed points of shift-invariant spaces generated by Gaussian kernel and hyperbolic secant
Markus Valås Hagen, Alexander Ulanovskii, Denis Zelent +1
We characterize the extreme and exposed points of the unit ball (with respect to the -norm) in the shift-invariant space generated by the Gaussian function, as well as in the…
Stability of shifts, interpolation, and crystalline measures
Alexander Ulanovskii, Ilya Zlotnikov
Let be the quasi shift-invariant space generated by -shifts of a function , where is a separated set. F…
Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
Alexander Ulanovskii, Ilya Zlotnikov
We introduce two families of generators (functions) that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical…
Sampling in the shift-invariant space generated by the bivariate Gaussian function
José Luis Romero, Alexander Ulanovskii, Ilya Zlotnikov
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the pla…
Contractive projections in Paley-Wiener spaces
Aleksei Kulikov, Ilya Zlotnikov
Let and be disjoint finite unions of parallelepipeds. We describe necessary and sufficient conditions on the sets and exponents such that the canonical pr…
On geometry of the unit ball of Paley-Wiener space over two symmetric intervals
Alexander Ulanovskii, Ilya Zlotnikov
Let be the space of integrable functions on whose Fourier transform vanishes outside , where , . In the case , we prese…