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arXiv · 1506.06499

Weighted Bergman-Dirichlet and Bargmann-Dirichlet spaces of order $m$ in high dimensions

Ayman El Fardi·Allal Ghanmi·Ahmed Intissar·Mohammed Ziyat
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Abstract

We introduce and study a generalization of the classical weighted Bergman and Dirichlet spaces on the unit ball in high dimension, the Bergman-Dirichlet spaces. Their counterparts on the whole $n$-complex space, the Bargmann-Dirichlet spaces, are also introduced and studied. Mainly, we give a complete description of the considered spaces, including orthonormal basis and the explicit formulas for their reproducing kernel functions. Moreover, we investigate their asymptotic behavior when the curvature goes to $0$.

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Ayman El Fardi, Allal Ghanmi, Ahmed Intissar, Mohammed Ziyat. 2015-06-22. Weighted Bergman-Dirichlet and Bargmann-Dirichlet spaces of order $m$ in high dimensions. https://arxiv.org/abs/1506.06499

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