April 16, 2024Open Access

Differential operators on Bergman space on bounded symmetric domains

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Abstract

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the N-dimensional unit ball BN and D² of 22 complex matrices satisfying I-ZZ^*>0. Our main tools are the discrete series representations of SU (N, 1) and SU (2, 2). We believe that our observations extend to general bounded symmetric domains.

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Christensen et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6f03ab6db64358766a8db https://doi.org/https://doi.org/10.48550/arxiv.2404.10882

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