АНАЛИТИЧЕСКОЕ ПРОДОЛЖЕНИЕ ФУНКЦИЙ, ЗАДАННЫХ НА ЧАСТИ ГРАНИЦЫ

Аннотация

Subject of the inquiry: scparatcly-analytical functions, holomorphic functions, pluriharmonic functions, separately-harmonic functions, subharmonic function. Aim of the inquiry: to determinate of the domain of holomorphicity of the scparatcly-analytic functions from the piece of the boundary; to study analytically continuability of functions defined on a pencil of boundary complex line; to study continuation of the pluriharmonic functions in a fixed direction; Z” 1 < P< °O to describe structure of singular sets of subharmonic functions from p , class. Methods of inquiry: methods of theory of functions of several complex variables, complex theory of potential and theory of analytical spaces. Achieved results and their novelty: - determined a domains of holomorphy of scparately-analytic and separately-harmonic functions defined on a piece of boundary; studied analytic continuation of holomorphic and pluriharmonic functions in a fixed direction; described the structure of singular sets of subharmonic functions from Lmp,\<p<<oo class through Cq.m - capacity. All proved theorems are new Practical value: dissertation has a theoretical character. Applications and economical efficiency: presented methods and results can be used for the further developing of the functions theory. They also can be useful in the applications of the complex analysis. Area of application: the theory of functions of complex variable and its application.