IJPAM: Volume 88, No. 1 (2013)
Department of Mathematics
Faculty of Science
Chonburi, 20131, THAILAND
Centre of Excellence in Mathematics
CHE, Si Ayutthaya Rd., Bangkok 10400, THAILAND
Abstract. This paper show that the space of rotation-invariant -functions with respect to a Gaussian measure can established as an even -space on with respect to some non-Gaussian measure. The space of holomorphic rotation-invariant -functions with respect to a complex Gaussian measure can established as a holomorphic even -space on with respect to some non-complex Gaussian measure. We give a condition for a rotation-invariant function which the image of the Segal-Bargmann transform to be in the space of holomorphic rotation-invariant -functions with respect to a complex Gaussian measure.
Received: July 11, 2013
AMS Subject Classification: Segal-Bargmann transform, Segal-Bargmann space, rotation-invariance
Key Words and Phrases: 81S30, 22E30, 60H30
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DOI: 10.12732/ijpam.v88i1.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395