IJPAM: Volume 88, No. 1 (2013)

ROTATION-INVARIANT $L^p$-FUNCTIONS

Areerak Chaiworn$^1$, Pheerachate Bunpatcharajarurn$^2$
$^1$Department of Mathematics
Faculty of Science
Burapha University
Chonburi, 20131, THAILAND
$^2$Centre of Excellence in Mathematics
CHE, Si Ayutthaya Rd., Bangkok 10400, THAILAND


Abstract. This paper show that the space of rotation-invariant $L^p$-functions with respect to a Gaussian measure can established as an even $L^p$-space on $\R$ with respect to some non-Gaussian measure. The space of holomorphic rotation-invariant $L^p$-functions with respect to a complex Gaussian measure can established as a holomorphic even $L^p$-space on $\C$ 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 $L^q$-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
Year: 2013
Volume: 88
Issue: 1