Holonomic functions in a polycircle with nonnegative imaginary part

  • V. S. Vladimirov
  • Yu. N. Drozhzhinov


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.


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations