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On the extension of a generalized differentiation operator

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Abstract

A generalized differentiation operator introduced by A. F. Leont'ev is considered in this note. The concept of an LD-operator is introduced, and necessary and sufficient conditions are determined for the extension of a generalized differentiation operator to some LD-operator.

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Literature cited

  1. A. F. Leont'ev, “The construction of a functional equation with a given system of particular solutions,” Dokl. Akad. Nauk SSSR,160, No. 1, 36–39 (1965).

    Google Scholar 

  2. A. O. Gel'fond and A. F. Leont'ev, “A generalized Fourier series,” Matem. Sb.,29, No. 3, 477–500 (1951).

    Google Scholar 

  3. A. F. Leont'ev, “On the region of regularity of the limit function of a sequence of analytic functions,” Matem. Sb.,39, No. 4, 405–420 (1956).

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  4. Yu. F. Korobeinik, “On generalized differentiation operators applied to any analytic function,” Izv. Akad. Nauk SSSR. Ser. Matem.,28, No. 4, 833–854 (1964).

    Google Scholar 

  5. A. I. Markushevich, The Theory of Analytic Functions, [in Russian], Vol. 2, Moscow (1968), Supplement.

  6. V. V. Napalkov, “On the extension of a generalized differentiation operator,” Matem. Sb.,78, No. 3, 399–409 (1969).

    Google Scholar 

  7. M. G. Khaplanov, “Some properties of an analytic space,” Dokl. Akad. Nauk SSSR,79, No. 6, 929–932 (1951).

    Google Scholar 

  8. L. Bieberbach, Analytic Continuation [Russian translation], Moscow (1967).

  9. G. Köthe, “Qualität in der Funktiontheorie,” J. reine u. angew. Math.,191, Nos. 1–2, 30–49 (1953).

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Authors and Affiliations

  1. Moscow Power Institute, USSR

    V. V. Napalkov

Authors
  1. V. V. Napalkov
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Additional information

Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 425–436, October, 1969.

The present work was completed under the direction of A. F. Leont'ev to whom the author expresses much gratitude.

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Napalkov, V.V. On the extension of a generalized differentiation operator. Mathematical Notes of the Academy of Sciences of the USSR 6, 710–716 (1969). https://doi.org/10.1007/BF01093807

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  • DOI: https://doi.org/10.1007/BF01093807

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