We study spaces of analytic functions generated by homogeneous polynomials from the dual space to the symmetric Hilbertian tensor product of a Hilbert space. In particular, we introduce an analogue of the classical Hardy space H² on the Hilbert unit ball and investigate spectral decomposition of unitary operators on this space. Also we prove a Wiener-type theorem for an algebra of analytic functions on the Hilbert unit ball.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-2-2,
author = {O. V. Lopushansky and A. V. Zagorodnyuk},
title = {Hilbert spaces of analytic functions of infinitely many variables},
journal = {Annales Polonici Mathematici},
volume = {81},
year = {2003},
pages = {111-122},
zbl = {1036.46030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-2-2}
}
O. V. Lopushansky; A. V. Zagorodnyuk. Hilbert spaces of analytic functions of infinitely many variables. Annales Polonici Mathematici, Tome 81 (2003) pp. 111-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap81-2-2/