2025/06/04 by Anirban Sen, Somdatta Barik, Sen, Anirban +3 · 1 citation
Mathematics · #47B32 #47B33 #47B35 #47B38 #Algebraic and Geometric Analysis #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Secondary: 47A05
paper · pdf · doi:10.48550/arxiv.2506.04052
openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we completely characterize the Berezin range of Toeplitz operators with harmonic symbols acting on weighted Bergman spaces, illustrating the necessity of the harmonicity condition through examples. We then introduce a new class of weighted composition operators on these spaces, investigating their fundamental properties and determining their Berezin range and Berezin number. Finally, we study the convexity of the Berezin range of composition operators on weighted Bergman spaces and show that the origin lies in its closure of Berezin range but not in the range itself.