English

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 Wμ\mathcal{W}_\mu and its truncated version Wμ\mathcal{W}'_\mu. 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 {ζ:ζ1<1}\{\zeta : |\zeta-1|<1\} 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