2 citations · 3 across the 10 of their papers we have counts for
12 papers
Methods of Construction of Exponential Bases on Planar Domains Revised
Oleg Asipchuk, Laura De Carli
In [1], we surveyed classical and recent results on the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We also construc…
Fourier sampling on a lattice
Oleg Asipchuk, Sinai Robins
We characterize the ambiguity in reconstructing bounded measurable sets from their Fourier transforms sampled on a lattice. For a full-rank lattice \(\mathcal L\subset\R^d\), we pr…
Rigidity in the planar Ulam floating body problem with perimetral densities under central symmetry
Oleg Asipchuk, Maksim Kosmakov, Pavel Zatitskii
We prove that the only planar, centrally symmetric, strictly convex body with boundary that floats in equilibrium in every orientation for the perimetr…
Block-equivalent finite Gabor frames
Oleg Asipchuk, Laura De Carli, Luis Rodriguez
We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal mat…
Rigidity in the Planar Ulam Floating Body Problem with perimetral density
Oleg Asipchuk, Maksim Kosmakov, Pavel Zatitskii
We study the two-dimensional Ulam's floating body problem for convex domains with perimetral density . Using the framework of Zindler carousels, we reduce the problem t…
Note on Robins' Conjecture in Dimension Four and Higher
Oleg Asipchuk
This article is motivated by a conjecture proposed by Sinai Robins in 2024. The conjecture asserts that two convex, centrally symmetric sets of positive measure that are not multi-…
Methods of construction of exponential bases on planar domains
Oleg Asipchuk, Laura De Carli
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with…
Exponential bases on modified domains
Oleg Asipchuk
The stability of exponential bases on domains in has been widely studied, with much of the research focusing on small perturbations of the phase. In this paper, we consider…
Concerning the stability of exponential systems and Fourier matrices
Oleg Asipchuk, Laura De Carli, Weilin Li
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result t…
Existence and non-existence of ground state solutions for magnetic NLS
Oleg Asipchuk, Christopher Leonard, Shijun Zheng
We show the existence and stability of ground state solutions (g.s.s.) for -critical magnetic nonlinear Schrödinger equations (mNLS) for a class of unbounded electromagnetic p…
Additive Stability of Frames
Oleg Asipchuk, Jacob Glidewell, Luis Rodriguez
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introdu…
Examples of exponential bases on Union of intervals
Oleg Asipchuk, Vladyslav Drezels
In this paper, we construct explicit exponential bases on finite or infinite unions of segments of total length one with some conditions on gaps between them. We also construct exp…