Berezin quantization and holomorphic representations
Berezin transform for non-scalar holomorphic discrete series
Let be a Hermitian symmetric space of the non-compact type and let be a discrete series representation of which is holomorphically induced from a unitary irreducible representation of . In the paper [B. Cahen, Berezin quantization for holomorphic discrete series representations: the non-scalar case, Beiträge Algebra Geom., DOI 10.1007/s13366-011-0066-2], we have introduced a notion of complex-valued Berezin symbol for an operator acting on the space of . Here we study the corresponding...
Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results.
Berezin-Weyl quantization for Cartan motion groups
We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].