DESCRIPTION OF SOME WEIGHTED EXPONENTIAL CLASSES OF SUBHARMONIC FUNCTIONS
ОПИСАНИЕ НЕКОТОРЫХ ВЕСОВЫХ ЭКСПОНЕНЦИАЛЬНЫХ КЛАССОВ СУБГАРМОНИЧЕСКИХ ФУНКЦИЙ

О.V. Okhlupina
2018 Bulletin of the South Ural State University series Mathematics Mechanics Physics  
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
more » ... uestion 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.
doi:10.14529/mmph180101 fatcat:li573yvgrjgs5bi6m6ggrwig3e