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arXiv · 2404.10882

Differential operators on {B}ergman space on bounded symmetric domains

Jens Gerlach Christensen·Christopher Benjamin Deng
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Abstract

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the $N$-dimensional unit ball $\mathbb{B}^N$ and $\mathbb{D}^2$ of $2\times2$ complex matrices satisfying $I-ZZ^*>0$.Our main tools are the discrete series representations of $\mathrm{SU}(N,1)$ and $\mathrm{SU}(2,2)$. We believe that our observations extend to general bounded symmetric domains.

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Jens Gerlach Christensen, Christopher Benjamin Deng. 2024-04-16. Differential operators on {B}ergman space on bounded symmetric domains. https://arxiv.org/abs/2404.10882

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