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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 810735, 7 pages
http://dx.doi.org/10.1155/2013/810735
Research Article

Hardy-Type Space Associated with an Infinite-Dimensional Unitary Matrix Group

Institute of Mathematics, University of Rzeszów, 16A Rejtana Street, 35-310 Rzeszów, Poland

Received 23 March 2013; Accepted 18 June 2013

Academic Editor: Qing-Wen Wang

Copyright © 2013 Oleh Lopushansky. 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

We investigate an orthogonal system of the homogenous Hilbert-Schmidt polynomials with respect to a probability measure which is invariant under the right action of an infinite-dimensional unitary matrix group. With the help of this system, a corresponding Hardy-type space of square-integrable complex functions is described. An antilinear isomorphism between the Hardy-type space and an associated symmetric Fock space is established.