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Holonomic functions in a polycircle with nonnegative imaginary part

  • V. S. Vladimirov
  • Yu. N. Drozhzhinov
Article
  • 28 Downloads

Abstract

A well-known theorem of Nevanlinna on the representation of nonnegative measure of a function holomorphic in a circle and having nonnegative imaginary part is extended to functions of many complex variables, holomorphic in a polycircle and having there a nonnegative imaginary part.

Keywords

Imaginary Part Complex Variable Nonnegative Measure Holonomic Function Nonnegative Imaginary Part 
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.
    R. Nevanlinna, Analytic Functions, Spring-Verlag (1969).Google Scholar
  2. 2.
    V. S. Vladimirov, Methods of the Theory of Functions of Many Complex Variables [in Russian], Moscow (1964).Google Scholar
  3. 3.
    G. E. Shilov and B. L. Gurevich. Integral, Measure, and Derivative [in Russian], Moscow (1967).Google Scholar
  4. 4.
    L. Schwartz, Mathematics for the Physical Sciences, Addison-Wesley (1967).Google Scholar
  5. 5.
    V. S. Vladimirov, “Holomorphic functions with nonnegative imaginary part in a tubular domain under a cone,” Matem. Sb.,79, No. 1, 128–152 (1969).Google Scholar
  6. 6.
    V. S. Vladimirov, “Holomorphic functions with positive imaginary part in a tube of the future,” Matem. Sb.,93, No. 1, 3–17 (1974).Google Scholar

Copyright information

© Consultants Bureau 1974

Authors and Affiliations

  • V. S. Vladimirov
    • 1
  • Yu. N. Drozhzhinov
    • 1
  1. 1.V. A. Steklov Mathematical InstituteAcademy of Sciences of the USSRUSSR

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