Hilbert spaces of analytic functions of infinitely many variables

Volume 81 / 2003

O. V. Lopushansky, A. V. Zagorodnyuk Annales Polonici Mathematici 81 (2003), 111-122 MSC: Primary 46G50; Secondary 46G20, 46G25. DOI: 10.4064/ap81-2-2

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 $H^2$ 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.

Authors

  • O. V. LopushanskyInstitute of Mathematics
    Cracow University of Technology
    Warszawska 24
    31-155 Kraków, Poland
    e-mail
  • A. V. ZagorodnyukInstitute for Applied Problems
    of Mechanics and Mathematics
    Ukrainian Academy of Sciences
    3b, Naukova St.
    79053, Lviv, Ukraine
    e-mail

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