The Conditions of Analytic Extendability of Functions Defined on a Part of the Boundary of Circular Domains

The paper is devoted to the conditions of existence of the holomorphic expansion, in a domain D, of a function f C (M) defined on a set M with a positive measure of the Shilov boundary S of the complete circular domain D C ⁿ . These conditions are as follows: integrals of the product of f by certain polynomials that are orthogonal holomorphic functions tend to 0.