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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 431-441
http://dx.doi.org/10.1155/S0161171290000655

Fourier transforms in generalized Fock spaces

Department of Mathematical Sciences, Box 2014, Oliver Hall, 1015 W. Main Street, Virginia Commonwealth University, Richmond 23284-2014, VA, USA

Received 16 June 1989

Copyright © 1990 Hindawi Publishing Corporation. 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.

Abstract

A classical Fock space consists of functions of the form,Φ(ϕ0,ϕ1,,ϕq,),where ϕ0C and ϕqL2(R3q), q1. We will replace the ϕq, q1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.