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Mathematics 2015, 3(3), 758-780; doi:10.3390/math3030758

The Segal–Bargmann Transform for Odd-Dimensional Hyperbolic Spaces

1
Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, USA
2
Department of Mathematics, Robert Morris University, 6001 University Boulevard, Moon Township, PA 15108, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Palle E.T. Jorgensen
Received: 7 July 2015 / Revised: 7 August 2015 / Accepted: 10 August 2015 / Published: 18 August 2015
(This article belongs to the Special Issue Mathematical physics)
View Full-Text   |   Download PDF [297 KB, uploaded 18 August 2015]   |  

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. View Full-Text
Keywords: Segal–Bargmann transform; heat kernel; hyperbolic space; spherical function Segal–Bargmann transform; heat kernel; hyperbolic space; spherical function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Hall, B.C.; Mitchell, J.J. The Segal–Bargmann Transform for Odd-Dimensional Hyperbolic Spaces. Mathematics 2015, 3, 758-780.

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