Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2011; 48(5): 1003-1014

Printed September 1, 2011

https://doi.org/10.4134/BKMS.2011.48.5.1003

Copyright © The Korean Mathematical Society.

Convolutions of white noise operators

Un Cig Ji and Young Yi Kim

Chungbuk National University, Chungbuk National University

Abstract

Motivated by the convolution product of white noise functionals, we introduce a new notion of convolution products of white noise operators. Then we study several interesting relations between the convolution products and the quantum generalized Fourier-Mehler transforms, and study a quantum-classical correspondence.

Keywords: white noise operator, Wick product, convolution, quantum generalized Fourier-Mehler transform

MSC numbers: Primary 60H40; Secondary 46F25