Berezin symbols and some problems on the Dirichlet space

Ulaş Yamancı ()
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Ulaş Yamancı: Suleyman Demirel University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1269-1277

Abstract: Abstract In this article, we characterize the classes $$S_{p}^{w}$$ S p w classes in terms of the boundary behavior of Berezin symbols of the weighted shift operators on the Dirichlet space $${\mathcal {D}}\left( {\mathbb {D}}\right) $$ D D . Also, we give a result related with the asymptotic multiplicative property of the Berezin symbol of any operator on reproducing kernel Hilbert space. Moreover, by using Berezin symbols, we give some condition for st- $$\left( DL\right) $$ D L convergence of a series of complex numbers.

Keywords: Berezin symbol; Compact operator; Reproducing kernel Hilbert space; Dirichlet space; Primary 47B32; Secondary 40D09 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-024-00553-z

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