Completeness of exponential systems in spaces of functions on a compact or domain and their area
Complex Variables
2023-06-29 v1
Abstract
We present new completeness conditions for exponential systems on the complex plane in Banach algebras of continuous functions on a compact with a connected complement that are simultaneously holomorphic in the interior of this compact if it is nonempty, as well as in spaces of holomorphic functions on a simply connected bounded domain with a topology of uniform convergence on compact subsets. These conditions are formulated in terms of the Euclidean area of the convex hull of a compact or a region on the one hand, and new characteristics of the distribution of exponential system indicators on the other.
Keywords
Cite
@article{arxiv.2306.15899,
title = {Completeness of exponential systems in spaces of functions on a compact or domain and their area},
author = {B. N. Khabibullin and E. G. Kudasheva},
journal= {arXiv preprint arXiv:2306.15899},
year = {2023}
}
Comments
10 pages, in Russian