Hilbert spaces of analytic functions of infinitely many variables

O. V. Lopushansky, and A. V. Zagorodnyuk. "Hilbert spaces of analytic functions of infinitely many variables." Annales Polonici Mathematici 81.2 (2003): 111-122. <http://eudml.org/doc/280391>.

@article{O2003,
abstract = {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.},
author = {O. V. Lopushansky, A. V. Zagorodnyuk},
journal = {Annales Polonici Mathematici},
keywords = {Hardy classes on the Hilbert ball; Wiener-type theorem},
language = {eng},
number = {2},
pages = {111-122},
title = {Hilbert spaces of analytic functions of infinitely many variables},
url = {http://eudml.org/doc/280391},
volume = {81},
year = {2003},
}

TY - JOUR
AU - O. V. Lopushansky
AU - A. V. Zagorodnyuk
TI - Hilbert spaces of analytic functions of infinitely many variables
JO - Annales Polonici Mathematici
PY - 2003
VL - 81
IS - 2
SP - 111
EP - 122
AB - 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.
LA - eng
KW - Hardy classes on the Hilbert ball; Wiener-type theorem
UR - http://eudml.org/doc/280391
ER -