Weyl calculus for complex and real symmetric domains. (English) Zbl 1150.43302

The paper under review generalizes the notion of the Weyl calculus of pseudodifferential operators acting on functions defined in a Euclidean domain, to the case of operators acting on holomorphic functions defined on real symmetric domains. The main result of the paper is the computation of the Weyl transform for all symmetric spaces of rank 1 and dimension \(n\).


43A85 Harmonic analysis on homogeneous spaces
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)