Hilbert spaces of analytic functions of infinitely many variables
Tom 81 / 2003
Annales Polonici Mathematici 81 (2003), 111-122
MSC: Primary 46G50; Secondary 46G20, 46G25.
DOI: 10.4064/ap81-2-2
Streszczenie
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 $H^2$ 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.
