6 papers · 1 filter
A note on a sparse sampling conjecture
Oleg Asipchuk, Sinai Robins
A conjecture made by the second author was that two convex, centrally symmetric bodies of positive measure which are not multi-tilers must agree up to a rigid motion whenever the F…
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…
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…
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…