Berezin quantization and holomorphic representations
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].
Bounding hyperbolic and spherical coefficients of Maass forms
We develop a new method to bound the hyperbolic and spherical Fourier coefficients of Maass forms defined with respect to arbitrary uniform lattices.