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UNITARITY OF KUO'S FOURIER–MEHLER TRANSFORM

Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, 361-763, Korea

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and

NOBUAKI OBATA

Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan

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https://doi.org/10.1142/S0219025704001487Cited by:5 (Source: Crossref)

Abstract

Kuo's Fourier–Mehler transforms {ℱ_Θ} form a one-parameter automorphism group of the space of white noise distributions . The adjoint transforms form a one-parameter automorphism group of the space of test white noise functions but do not admit unitary extensions with respect to the L²-norm induced from the Gaussian measure with variance 1. We prove that admits an extension to a one-parameter group of unitary operators on the L²-space with respect to the Gaussian measure with variance 1/2.

Keywords:

AMSC: primary 60H40, secondary 46F25

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