Differential operators on Bergman space on bounded symmetric domains

2024/04/16 by Jens Gerlach Christensen, Christensen, Jens Gerlach, Christopher Benjamin Deng +1
Mathematics · #32A36 #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2404.10882

openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify self-adjoint first-order differential operators on weighted Bergman spaces on the N-dimensional unit ball \mathbbB^N and \mathbbD² of 2×2 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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