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Ukrainian Mathematical Journal

, Volume 28, Issue 2, pp 130–138 | Cite as

The Feynman integral and expansions in eigenfunctions of the Schrödinger operator

  • G. N. Gestrin
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Literature cited

  1. 1.
    L. D. Faddeev, “The Feynman integral for singular Lagrangians,” Teor. i Matem. Fiz.,1, No.1 (1969).Google Scholar
  2. 2.
    L. D. Faddeev and V. N. Popov, “Covariant quantization of the gravitational field,” Usp. Fiziol. Nauk,3, No. 3 (1973).Google Scholar
  3. 3.
    D. I. Blokhintsev and B. M. Barbashov, “Applications of functional integrals in quantum mechanics and field theory,” Usp. Fiziol. Nauk, 106, No. 4 (1972).Google Scholar
  4. 4.
    Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators, Amer. Math. Soc. (1968).Google Scholar
  5. 5.
    T. Kato, Perturbation Theory of Linear Operators, Springer-Verlag (1966).Google Scholar
  6. 6.
    A. Yu. Povzner, “On the expansion of functions in the eigenfunctions of the operator Δu + cu,” Matem. Sbornik,32 (74), No. 1 (1953).Google Scholar
  7. 7.
    Ya. L. Daletskii, “Integrals in function spaces,” Itogi Nauki, Matematicheskii Analiz 1936, Moscow (1967).Google Scholar
  8. 8.
    E. Nelson, “Feynman integrals and the Schrödinger equation,” J. Math. Phys.,5, No. 3 (1964).Google Scholar
  9. 9.
    G. N. Gestrin, “On the Feynman integral,” in: Theory of Functions, Functional Analysis, and Applications, No. 12 (1970).Google Scholar
  10. 10.
    J. L. B. Cooper, “One-parameter semigroups of isometric operators in Hilbert space,” Annals of Math.,48, No. 4 (1947).Google Scholar
  11. 11.
    B. Simon, “Essential self-adjointness of Schrödinger operators with positive potentials,” Math. Ann. Band, 201, No. 3, 211–220 (1973).Google Scholar
  12. 12.
    T. Kato, “Schrodinger operators with Singular potentials,” RZh Mat., Review B 669,9 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • G. N. Gestrin
    • 1
  1. 1.Physical-Technical Institute of Low Temperature PhysicsAcademy of Sciences of the Ukrainian SSRUSSR

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