Segal-Bargmann transforms from hyperbolic Hamiltonians

The Segal–Bargmann Transform for Odd-Dimensional Hyperbolic Spaces

We develop isometry and inversion formulas for the Segal–Bargmann transform on odd-dimensional hyperbolic spaces that are as parallel as possible to the dual case of odd-dimensional spheres.

Laplace and Segal-bargmann Transforms on Hermitian Symmetric Spaces and Orthogonal Polynomials

Segal-bargmann Transforms of One-mode Interacting Fock Spaces Associated with Gaussian and Poisson Measures

Let μg and μp denote the Gaussian and Poisson measures on R, respectively. We show that there exists a unique measure μ̃g on C such that under the Segal-Bargmann transform Sμg the space L (R, μg) is isomorphic to the space HL(C, μ̃g) of analytic L-functions on C with respect to μ̃g . We also introduce the Segal-Bargmann transform Sμp for the Poisson measure μp and prove the corresponding result. A...

Segal–bargmann Transform for Compact Quotients

Abstract. Let G be a connected complex semisimple group, assumed to have trivial center, and let K be a maximal compact subgroup of G. Then G/K, with a fixed G-invariant Riemannian metric, is a Riemannian symmetric space of the complex type. Now let Γ be a discrete subgroup of G that acts freely and cocompactly on G/K. We consider the Segal–Bargmann transform, defined in terms of the heat equat...

The Segal Bargmann Transform for Path-Groups

Let K be a connected Lie group of compact type and let W(K ) denote the set of continuous paths in K, starting at the identity and with time-interval [0, 1]. Then W(K ) forms an infinite-dimensional group under the operation of pointwise multiplication. Let \ denote the Wiener measure on W(K ). We construct an analog of the Segal Bargmann transform for W(K ). Let KC be the complexification of K...