Radial Toeplitz operators on the weighted Bergman spaces of Cartan domains

TL;DR

This paper provides explicit formulas for diagonalizing Toeplitz operators with symmetric symbols on weighted Bergman spaces of all irreducible bounded symmetric domains, including exceptional cases.

Contribution

It offers a comprehensive explicit diagonalization method for Toeplitz operators with K-invariant symbols on weighted Bergman spaces of Cartan domains, covering all types including exceptional ones.

Findings

Explicit diagonalization formulas for Toeplitz operators provided.

Formulas applicable to all irreducible bounded symmetric domains.

Includes detailed cases for exceptional domains.

Abstract

Let $D$ be an irreducible bounded symmetric domain with biholomorphism group $G$ with maximal compact subgroup $K$. For the Toeplitz operators with $K$-invariant symbols we provide explicit simultaneous diagonalization formulas on every weighted Bergman space. The expressions are given in the general case, but are also worked out explicitly for every irreducible bounded symmetric domain including the exceptional ones.