Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group
Let be a Hermitian symmetric space of the noncompact type and let be a discrete series representation of holomorphically induced from a unitary character of . Following an idea of Figueroa, Gracia-Bondìa and Vàrilly, we construct a Stratonovich-Weyl correspondence for the triple by a suitable modification of the Berezin calculus on . We extend the corresponding Berezin transform to a class of functions on which contains the Berezin symbol of for in the Lie algebra of . This allows...
We construct and study a Stratonovich-Weyl correspondence for the holomorphic representations of the Jacobi group.
We prove Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on the Heisenberg group. A key point consists in estimating the decay in time of the norm of the free solution; this requires a careful analysis due also to the non-homogeneous nature of the full Laplacian.