The Segal--Bargmann transform for odd-dimensional hyperbolic spaces
Brian C. Hall, Jeffrey J. Mitchell
TL;DR
This paper develops isometry and inversion formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces, extending the understanding of this transform in non-compact symmetric spaces.
Contribution
It introduces new formulas for the Segal--Bargmann transform on odd-dimensional hyperbolic spaces, paralleling the sphere case, and advances the mathematical theory of harmonic analysis on these spaces.
Findings
Derived isometry formulas for the transform.
Established inversion formulas for the transform.
Extended the duality between hyperbolic spaces and spheres.
Abstract
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.
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