Localization operators on Bergman and Fock spaces

Release time:2026-03-09

Journal:arXiv:2603.04051

Abstract:We introduce localization operators on weighted Bergman and Fock spaces and show that, under a natural scaling of symbols and window functions, localization operators on the weighted Bergman space $A_{\beta r^2}^2$ converge, in the weak sense, to localization operators on the Fock space $F_{\beta}^2$ as $r\to\infty$. From this we derive several applications, including one about sharp norm estimates for certain Toeplitz operators on Fock spaces, one about windowed Berezin transforms for weighted Bergman spaces, and another about Szeg\"{o}-type theorems for localization operators on weighted Bergman spaces.

Co-author:Pan Ma, Fugang Yan, Dechao Zheng, Kehe Zhu

Indexed by:Journal paper

Translation or Not:no