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arXiv · 2307.05108

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

Safa Snoun·Noureddine Ghiloufi
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Abstract

In this paper, we start by introducing the modified Bergman-Dirichlet space $\mathcal D_m^2(\mathbb D_R,\mu^R_{\alpha,\beta})$ and then we study its asymptotic behavior when the parameter $\alpha$ 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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Safa Snoun, Noureddine Ghiloufi. 2023-07-11. Asymptotic results on modified Bergman-Dirichlet spaces and examples of Segal-Bargmann transforms. https://arxiv.org/abs/2307.05108

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