Ukrainian Mathematical Journal

, Volume 39, Issue 3, pp 264–270 | Cite as

Self-adjointness of elliptic operators in infinitely many variables

  • V. A. Liskevich
  • Yu. A. Semenov


Elliptic Operator 
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Literature cited

  1. 1.
    B. Simon, The (ϕ)2-Euclidean (Quantum) Field Theory, Princeton Univ. Press. (1974).Google Scholar
  2. 2.
    Yu. M. Berezanskii, “Self-adjointness of elliptic operators in infinitely many variables,” Ukr. Mat. Zh.,27, No. 6, 729–742 (1975).Google Scholar
  3. 3.
    Yu. M. Berezanskii, Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables [in Russian], Naukova Dumka, Kiev (1978).Google Scholar
  4. 4.
    M. A. Perel'muter and Yu. A. Semenov, “Self-adjointness of elliptic operators with a finite or infinite number of variables,” Funkts. Anal. Prilozhen.,14, No. 1, 81–82 (1980).Google Scholar
  5. 5.
    B. Simon, “A canonical decomposition for quadratic forms with applications to monotone theorems,” J. Funct. Anal.,28, No. 3, 377–385 (1978).Google Scholar
  6. 6.
    M. Reed, “On self-adjointness in infinite tensor product spaces,” J. Funct. Anal.,5, No. 1, 94–124 (1970).Google Scholar
  7. 7.
    N. Dunford and J. T. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York (1958).Google Scholar
  8. 8.
    T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-New York (1966).Google Scholar
  9. 9.
    V. F. Kovalenko and Yu. A. Semenov, “Some questions concerning the expansion in generalized eigenfunctions of the Schrödinger operator with strongly singular potentials,” Usp. Mat. Nauk,33, No. 4, 107–140 (1978).Google Scholar
  10. 10.
    Yu. A. Semenov, “Smoothness of the generalized solutions of the equation\((\lambda - \mathop \Sigma \limits_{ii} \nabla _i \alpha _{ij} \nabla _j ) u = f\) with continuous coefficients,” Mat. Sb.,118, No. 3, 399–410 (1982).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • V. A. Liskevich
    • 1
  • Yu. A. Semenov
    • 1
  1. 1.Kiev Polytechnic InstituteUSSR

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