Asymptotic results on modified Bergman-Dirichlet spaces and examples of Segal-Bargmann transforms

2023/07/11 by Safa Snoun, Snoun, Safa, Noureddine Ghiloufi +1
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2307.05108

Abstract

In this paper, we start by introducing the modified Bergman-Dirichlet space \mathcal D_m²(\mathbb D_R,μ^R_α,β) and then we study its asymptotic behavior when the parameter α goes to infinity and to (-1) to obtain respectively the modified Bargmann-Dirichlet and the modified Hardy-Dirichlet spaces with their reproducing kernels. Finally, we give some examples of Segal-Bargmann transforms of those spaces.

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