Hilbert spaces for certain unipotent representations III

T ] 1 3 A pr 1 99 9 Explicit Hilbert spaces for certain unipotent representations II

Explicit Hilbert spaces for certain unipotent representations

Let G be the universal cover of the group of automorphisms of a symmetric tube domain and let P = L N be its Shilov boundary parabolic subgroup. This paper attaches an irreducible unitary representation of G to each of the (finitely many) L-orbits on n*. The Hilbert space of the representation consists of functions on the orbit which are square-integrable with respect to a certain L-equivariant...

Explicit Hilbert spaces for certain unipotent representations II

To each real semisimple Jordan algebra, the Tits-Koecher-Kantor theory associates a distinguished parabolic subgroup P = L N of a semisimple Lie group G. The groups P which arise in this manner are precisely those for which N is abelian, and P is conjugate to its opposite P. Each non-open L-orbit O on N∗ admits an L-equivariant measure dμ which is unique up to scalar multiple. By Mackey theory,...

F eb 2 00 3 Representation of Semigroups in Rigged Hilbert Spaces : Subsemigroups of the Weyl - Heisenberg Group

This paper studies how differentiable representations of certain subsemigroups of the Weyl-Heisenberg group may be obtained in suitably constructed rigged Hilbert spaces. These semigroup representations are induced from a continuous unitary representation of the Weyl-Heisenberg group in a Hilbert space. Aspects of the rigged Hilbert space formulation of time asymmetric quantum mechanics are als...

G-frames and their duals for Hilbert C*-modules

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...