5 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…
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…
Contractive Hardy--Littlewood inequalities in the Dirichlet range
Ole Fredrik Brevig, Aleksei Kulikov, Kristian Seip +1
The class consists of those analytic functions in the unit disc such that \[\|f\|_{α,p}^p := |f(0)|^p+\int_0^1 \left(\frac{d}{dr} M_p^p(r,f)\right) (1-r^2)^{α-1} \,dr <…
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…