THEORY OF KHARTOGS SERIES AND HOLOMORPHIC FUNCTIONS
Keywords:
Hartogs series, holomorphic functions, analytic extension, plurisubharmonic functions, absolute convergence, uniform convergence, functions of complex variables, complex analysis, mathematical physics.Abstract
This article examines Hartogs series, which play a crucial role in the theory of functions of several complex variables. The problems of analytical continuation of holomorphic functions and their convergence through Hartogs series are considered. The article proves the absolute and uniform convergence of Hartogs series and shows their relationship with plurisubharmonic functions. Also, the importance of Hartogs series in the study of holomorphic functions and their application are explained with examples. The research results offer new approaches that can be applied in the fields of complex analysis and mathematical physics.
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