Completeness on the worm domain and the M\"untz-Sz\'asz problem for the Bergman space
Complex Variables
2020-09-08 v2
Abstract
In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain and its truncated version . We determine some orthogonal systems and show that they are not complete, while showing that the union of two particular of such systems is complete. In order to prove our completeness result we introduce the Muentz-Szasz problem for the 1-dimensional Bergman space of the disk and find a sufficient condition for its solution.
Keywords
Cite
@article{arxiv.1509.06383,
title = {Completeness on the worm domain and the M\"untz-Sz\'asz problem for the Bergman space},
author = {Steven G. Krantz and Marco M. Peloso and Caterina Stoppato},
journal= {arXiv preprint arXiv:1509.06383},
year = {2020}
}
Comments
14 pages, Author Accepted Manuscript