Poly-Fock Spaces

  • N. L. Vasilevski
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 117)


Consider the space L 2(ℂn, dµn), where dµn is the Gaussian measure, and its Fock subspace F2(ℂn) consisting of all analytic (entire) functions in ℂn. We introduce the so-called truepoly-Fock spaces, and prove that L 2 (ℂn, dµn) is the direct sum of the Fock and all true-polyFock spaces.

AMS Classification

46E20 46E22 81S05 


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  1. [1]
    V. Bargmann, On a Hilbert space of analytic functions. Comm. Pure Appl. Math. 3 (1961), 215–228.MathSciNetGoogle Scholar
  2. [2]
    Harry Bateman and Arthur Erdélyi, Higher transcendental functions, vol. 2. McGraw-Hill, 1954.Google Scholar
  3. [3]
    F.A. Berezin, Covariant and contravariant symbols of operators. Math. USSR Izvestia 6 (1972), 1117–1151.CrossRefGoogle Scholar
  4. [4]
    V.A. Fock, Konfigurationsraum and zweite Quantelung. Z. Phys. 75 (1932), 622–647.CrossRefGoogle Scholar
  5. [5]
    I.S. Gradshteyn and I.M. Ryzhik, Tables of Integrals, Series, and Products. Academic Press, New York, 1980.Google Scholar
  6. [6]
    I.E. Segal, Lectures at the Summer Seminar on Appl. Math. Boulder, Colorado, 1960.Google Scholar
  7. [7]
    Sundaram Thangavelu, Lectures on Hernatte and Laguerre expansions. Princeton University Press, Preiceton, New Jersey, 1993.Google Scholar

Copyright information

© Springer Basel AG 2000

Authors and Affiliations

  • N. L. Vasilevski
    • 1
  1. 1.Departamento de MatemáticasCinvestav del I.P.N.México, D.F.México

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