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On Multidimensional Integral Operators

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Linear Operators and Operator Equations

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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]).

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Literature Cited

  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.

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  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.

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  3. M. Sh. Birman and M. Z. Solomyak, “On estimates of the singular numbers of integral operators. II,” Vestnik LGU, No. 13 (1967).

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  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).

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  5. M. Z. Solomyak and V. V. Sten’kin, “On one class of Stieltjes multiple-integral operators,” Present volume, p. 99.

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  6. E. Hille and R. Phillips, Functional Analysis and Semigroups [Russian translation], IL, Moscow (1951), pp. 60-64.

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  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).

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  8. S. M. Nikol’skii, “On theorems of imbedding, extension, and approximation,” Uspekhi Matem. Nauk, Vol. 16, No. 3(101), pp. 63–114 (1961).

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Authors
  1. B. S. Pavlov
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Editors and Affiliations

  1. Leningrad State University, Russia

    V. I. Smirnov

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© 1971 Consultants Bureau, New York

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Pavlov, B.S. (1971). On Multidimensional Integral Operators. In: Smirnov, V.I. (eds) Linear Operators and Operator Equations. Problems in Mathematical Analysis / Problemy Matematicheskogo Analiza / Πроблемы Математического Анализа. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0013-8_4

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  • DOI: https://doi.org/10.1007/978-1-4757-0013-8_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0015-2

  • Online ISBN: 978-1-4757-0013-8

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