Oleg Asipchuk

activity

20242026

collaborators

8 papers

math.MG2026

Rigidity in the planar Ulam floating body problem with perimetral densities $I ¨ = \frac{1}{8}, \frac{3}{8}$ under central symmetry

Oleg Asipchuk, Maksim Kosmakov, Pavel Zatitskii

We prove that the only planar, centrally symmetric, strictly convex body $K \subset R^{2}$ with $C^{1}$ boundary that floats in equilibrium in every orientation for the perimetr…

math.FA2026

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…

math.MG2026

Rigidity in the Planar Ulam Floating Body Problem with perimetral density $I ¨ = \frac{1}{6}$

Oleg Asipchuk, Maksim Kosmakov, Pavel Zatitskii

We study the two-dimensional Ulam's floating body problem for convex domains with perimetral density $I ¨ = \frac{1}{6}$ . Using the framework of Zindler carousels, we reduce the problem…

math.FA2025

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-…

math.CA2025

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…

math.FA2025

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…