Toeplitz quantization and asymptotic expansions for real bounded symmetric domains
This paper introduces a certain star restriction for the setting of real bounded symmetric domains. Let us recall that geometric quantizations of complex Kähler manifolds are very useful to study symmetric manifolds. In this case, the product of observables is described via the Weyl calculus and the Toeplitz-Berezin calculus. In this work, the authors ``generalise'' these notions to the framework of real symmetric manifolds. They introduce an analogue star operator, called star restriction. They prove the usual asymptotic expansion of this star restriction. Moreover, they establish an analogue of the theorem of Arazy and Orsted related to the Berezin transform.
scientific article; zbMATH DE number 5944196
scientific article