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Abstract

In a number of problems of operator theory, it is necessary to investigate integral operators of the form
$$ \int {\int {\varphi (\lambda ,\mu )d{E_\lambda }Td{E_\mu }.} } $$
. Such integral operators have been studied in a number of articles by M. Sh. Birman and M. Z. Solomyak ([1], [2], [3]).

Keywords

Integral Operator Elementary Extension Piecewise Polynomial Function Degenerate Function Special Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature Cited

  1. 1.
    M. Sh. Birman and M. Z. Solomyak, “Stieltjes double-integral operators,” in: Topics in Mathematical Physics, Vol. 1, M. Sh. Birman (editor), Consultantus Bureau, New York (1967), p. 25.Google Scholar
  2. 2.
    M. Sh. Birman and M. Z. Solomyak, “Stieltjes double-integral operators. II,” in: Topics in Mathematical Physics, Vol. 2, M. Sh. Birman (editor), Consultants Bureau, New York (1968), p. 19.Google Scholar
  3. 3.
    M. Sh. Birman and M. Z. Solomyak, “On estimates of the singular numbers of integral operators. II,” Vestnik LGU, No. 13 (1967).Google Scholar
  4. 4.
    M. Sh. Birman and M. Z. Solomyak, “Piecewise polynomial approximations of functions belonging to classes Wα p,” Matem. Sbornik, Vol. 73, No. 3(115), pp. 50–74 (1967).Google Scholar
  5. 5.
    M. Z. Solomyak and V. V. Sten’kin, “On one class of Stieltjes multiple-integral operators,” Present volume, p. 99.Google Scholar
  6. 6.
    E. Hille and R. Phillips, Functional Analysis and Semigroups [Russian translation], IL, Moscow (1951), pp. 60-64.Google Scholar
  7. 7.
    V. P. Il’in and V. A. Solonnikov, “On some properties of differentiable functions of many variables,” Dokl. Akad. Nauk SSSR, Vol. 136, No. 3, pp. 538–544 (1961).MathSciNetGoogle Scholar
  8. 8.
    S. M. Nikol’skii, “On theorems of imbedding, extension, and approximation,” Uspekhi Matem. Nauk, Vol. 16, No. 3(101), pp. 63–114 (1961).Google Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • B. S. Pavlov

There are no affiliations available

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