Ukrainian Mathematical Journal

, Volume 24, Issue 4, pp 351–372 | Cite as

Positive definite functions of infinitely many variables in a layer

  • Yu. M. Berezanskii
  • I. M. Gali


Definite Function Positive Definite Function 
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Literature cited

  1. 1.
    M. G. Krein, “A general method of expansion of positive definite kernels into elementary products,” Dokl. Akad. Nauk SSSR,53, No. 1 (1946).Google Scholar
  2. 2.
    Yu. M. Berezanskii, Eigenfunction Expansions of Selfadjoint Operators [in Russian], Naukova Dumka, Kiev (1965).Google Scholar
  3. 3.
    Yu. M. Berezanskii, “Expansion in generalized eigenvectors and integral representation of positive definite kernels in the form of a continual integral,” Sibirsk. Matem. Zh.,9, No. 5 (1968).Google Scholar
  4. 4.
    Yu. M. Berezanskii, “Integral representation of positive definite functionals of Wightman type,” Ukrainsk. Matem. Zh.19, No. 1 (1967).Google Scholar
  5. 5.
    Yu. M. Berezanskii, “Representation of Wightman type functionals by continual integrals,” Funktsional'. Analiz i Ego Prilozhen.,3, No. 2 (1969).Google Scholar
  6. 6.
    Yu. M. Berezanskii and S. N. Shifrin, “Generalized power moment problem,” Ukrainsk. Matem. Zh.,23, No. 3 (1971).Google Scholar
  7. 7.
    R. A. Minlos, “Generalized random processes and their continuation to a measure,” Trudy Mosk. Matem. O-va,8 (1959).Google Scholar
  8. 8.
    V. V. Sazonov, “A remark on characteristic functionals,” Teoriya Veroyatnostei i Ee Primeneniya,3, No. 2 (1958).Google Scholar
  9. 9.
    A. Devinatz, “On the extensions of positive definite functions,” Acta Math.,102, Nos. 1–2, 109–134 (1959).Google Scholar
  10. 10.
    G. I. Éskin, “Sufficient condition of solvability of multidimensional moment problem,” Dokl. Akad. Nauk SSSR,133, No. 3 (1960).Google Scholar
  11. 11.
    Yu. M. Berezanskii, I. M. Gali, and V. A. Zhuk, “Positive definite functions of infinitely many variables,” Dokl. Akad. Nauk SSSR,203, No. 1 (1972).Google Scholar
  12. 12.
    N. N. Vakhaniya, “Characteristic functionals for random sequences,” in: Some Problems in the Theory of Stochastic Processes, Metsniereba, Tbilisi (1965).Google Scholar
  13. 13.
    J. Kuelbs and V. Mandrekar, “Harmonic analysis on certain vector spaces,” Trans. Amer. Math. Soc.,149, 213–231 (1970).Google Scholar
  14. 14.
    B. Ya. Levin and I. E. Ovcharenko, “Continuation of hermitian positive functions defined in a strip,” Teoriya Funktsii, Funktsional'nyi Analiz i Ego Prilozheniya, No. 5 (1967).Google Scholar
  15. 15.
    Yu. M. Berezanskii and M. L. Gorbachuk, “Continuation of positive definite functions to two variables,” Ukrainsk. Matem. Zh.,17, No. 5 (1965).Google Scholar
  16. 16.
    I. M. Gel'fand and N. Ya. Vilenkin, Applications of Harmonic Analysis. Equipped Hilbert Spaces [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  17. 17.
    M. Cotlar, Equipped Hilbert Spaces [in Spanish], University of Buenos Aires (1968).Google Scholar
  18. 18.
    K. Maurin, General Eigenfunction Expansions and Unitary Representations of Topological Groups, PMN, Warsaw (1968).Google Scholar
  19. 19.
    I. I. Gikhman and A. V. Skorokhod, Theory of Random Processes [in Russian], Vol. 1, Nauka, Moscow (1971).Google Scholar
  20. 20.
    Yu. L. Daletskii, “Integration in functional spaces,” Itogi Nauki, Matematicheskii Analiz, VINITI, Moscow (1967).Google Scholar
  21. 21.
    Yu. M. Berezanskii, “Generalized power moment problem,” Trudy Mosck. Matem. O-va,21 (1970).Google Scholar
  22. 22.
    P. Halmos, Measure Theory, Van Nostrand, New York (1950).Google Scholar
  23. 23.
    R. S. Ismagilov, “Selfadjoint extensions of a system of commuting symmetrical operators,” Dokl. Akad. Nauk SSSR,133, No. 3 (1960).Google Scholar
  24. 24.
    M. G. Krein, “Hermitian positive kernels on homogeneous spaces. Part1,” Ukrainsk. Matem. Zh. 1, No. 4 (1949).Google Scholar
  25. 25.
    G. E. Shilov and Fan Dyk Ting, Integral, Measure, and Derivative on Linear Spaces [in Russian], Nauka, Moscow (1967).Google Scholar
  26. 26.
    U. Dieudonné, Foundations of Modern Analysis, Academic Press, New York-London (1960).Google Scholar

Copyright information

© Consultants Bureau 1973

Authors and Affiliations

  • Yu. M. Berezanskii
    • 1
  • I. M. Gali
    • 1
  1. 1.Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR and Kiev State UniversityUSSR

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