Ukrainian Mathematical Journal

, Volume 41, Issue 8, pp 891–896 | Cite as

Abstract Plancherel equation and inversion formula

  • L. I. Vainerman


Inversion Formula Plancherel Equation 
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Literature cited

  1. 1.
    B. M. Levitan, Theory of Generalized Translation Operators [in Russian], Nauka, Moscow (1973).Google Scholar
  2. 2.
    Yu. M. Berezanskii and A. A. Kalyuzhnyi, “Hypercomplex systems with locally compact bases,” Selecta Math. Sov.,4, No. 2, 151–200 (1985).Google Scholar
  3. 3.
    L. I. Vainerman, “Duality of algebras with involution and generalized translation operators,” Itogi Nauki Tekh., Mathematical Analysis, VINITI,24, 165–205 (1986).Google Scholar
  4. 4.
    L. I. Vainerman and G. L. Litvinov, “The Plancherel formula and the inversion formula for generalized translation operators,” Dokl. Akad. Nauk SSSR,251, No. 4, 792–795 (1981).Google Scholar
  5. 5.
    J. Dixmier, Les Algebres d'Operateurs dans l'Espace Hilbertien, Gauthier-Villars, Paris (1969).Google Scholar
  6. 6.
    M. A. Naimark, Normed Rings [in Russian], Nauka, Moscow (1968).Google Scholar
  7. 7.
    A. Inoue, “On a class of unbounded operator algebras,” Pac. J. Math.,65, No. 1, 77–95 (1976);66, No. 2, 411–431 (1976);69, No. 1, 105–115 (1977).Google Scholar
  8. 8.
    I. Ts. Gokhberg and M. G. Krein, Theory of Volterra Operators in Hilbert Space and Its Applications [in Russian], Nauka, Moscow (1967).Google Scholar
  9. 9.
    A. Ya. Povzner, “On equations of Sturm-Liouville type on a semi-axis,” Dokl. Akad. Nauk SSSR,43, No. 9, 387–391 (1944).Google Scholar
  10. 10.
    Yu. M. Berezanskii, “On hypercomplex systems constructed from a Sturm-Liouville equation on a semi-axis,” Dokl. Akad. Nauk SSSR,91, No. 6, 1245–1248 (1953).Google Scholar
  11. 11.
    N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space [in Russian], Nauka, Moscow (1966).Google Scholar
  12. 12.
    L. Bers, F. John, and M. Schechter, Partial Differential Equations, Am. Math. Soc, Providence (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • L. I. Vainerman
    • 1
  1. 1.Kiev UniversityUSSR

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