Completeness on the worm domain and the Müntz-Szász problem for the Bergman space

Abstract

In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain ${\mathcal{W}}_{\mu }$ and its truncated version ${\mathcal{W}}_{\mu }^{\prime }$. 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 $\{\zeta :|\zeta -1|<1\}$ and find a sufficient condition for its solution.

14 pages, Author Accepted Manuscript

References in corpus (3)

• The Bergman kernel and projection on non-smooth worm domains
• Bergman kernel and projection on the unbounded worm domain
• Sharp estimates for the Szegő projection on the distinguished boundary of model worm domains

Cited by in corpus (4)

• Sharp estimates for the Szegő projection on the distinguished boundary of model worm domains
• Irregularity of the Bergman projection on smooth unbounded worm domains
• On a higher-dimensional worm domain and its geometric properties
• (Ir-)regularity of canonical projection operators on some weakly pseudoconvex domains