Description of some weighted exponential classes of subharmonic functions

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The role of subharmonic functions in such sections of analysis as complex and real analysis is very significant. Such classes of functions are closely related to analytic harmonic functions and make an important contribution to the general theory of potential and mathematical physics. In the works of R. Nevanlinna and W. Heiman, parametric representations of subharmonic classes in the plane of functions, whose characteristic has a power growth at infinity, are obtained. The question of whether similar representations are true for weighted classes that admit a stronger growth at infinity (for example, the exponential growth) arises in the theory of entire and meromorphic functions. In this article, classes of subharmonic functions with Nevanlinna characteristic that is summable with exponential weight in a complex plane are introduced for consideration, and the representing measures of functions of such classes are studied. When proving the results, methods of complex and functional analysis are used. An important role in the study is played by potentials based on the factors of the modified Weierstrass product. The proof of the main result is based on the use of auxiliary assertions formulated in the form of lemmas.


Subharmonic function, harmonic function, representing measures, thenevanlinna's characteristic

Короткий адрес:

IDR: 147158968   |   DOI: 10.14529/mmph180101

Список литературы Description of some weighted exponential classes of subharmonic functions

  • Hayman, W.K. Subharmonic functions/W.K. Hayman. -Acad. Press, London etc. -1989. -Vol. 2. -591 p.
  • Ронкин, Л.И. Введение в теорию целых функций многих переменных/Л.И. Ронкин. -М.: Наука, 1971. -432 с.
  • Азарин, В.С. Теория роста субгармонических функций/В.С. Азарин. -Харьков: ХГУ, 1982. -73 с.
  • Охлупина, О.В. Потенциалы типа Грина и интегральные представления весовых классов субгармонических функций: дис.... канд. физ.-мат. наук/О.В. Охлупина. -Брянск, 2012. -118 с.
  • Брело, М. Основы классической теории потенциала/М. Брело. -М.: Мир, 1964. -215 с.
  • Быков, С.В. О нулях целых функций с мажорантой бесконечного порядка/С.В. Быков, Ф.А. Шамоян//Алгебра и анализ. -Санкт-Петербургское отделение Института математики РАН им. В.А. Стеклова, СПб: Наука, 2009. -Т. 21, № 6. -С. 66-79.
  • Shamoyan, F.A. Topics in the theory of spaces/F.A. Shamoyan, A.E. Djrbashian//Teubner Texte zur Mathematik . -BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1988. -Vol. 105. -P. 200.
  • Шамоян, Ф.А. Введение в теорию весовых -классов мероморфных функций/Ф.А. Шамоян, Е.Н. Шубабко. -Брянск: РИО БГУ, 2009. -153 с.
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