In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain Wμ and its truncated version W'μ. 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: |ζ − 1| < 1} and find a sufficient condition for its solution.
Completeness on the worm domain and the Müntz–Szász problem for the Bergman space / Krantz S.G.; Peloso M.M.; Stoppato C.. - In: MATHEMATICAL RESEARCH LETTERS. - ISSN 1073-2780. - STAMPA. - 26:(2019), pp. 231-251. [10.4310/MRL.2019.v26.n1.a11]
Completeness on the worm domain and the Müntz–Szász problem for the Bergman space
Stoppato C.
2019
Abstract
In this paper we are concerned with the problem of completeness in the Bergman space of the worm domain Wμ and its truncated version W'μ. 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: |ζ − 1| < 1} and find a sufficient condition for its solution.
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