THE CONDITIONS OF ANALYTIC EXTENDABILITY OF FUNCTIONS DEFINED ON A PART OF THE BOUNDARY OF CIRCULAR DOMAINS


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Abstract

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 μ of the Shilov boundary S of the complete circular domain D ⊂ Cn. These conditions are as follows: integrals of the product of f by certain polynomials that are orthogonal holomorphic functions tend to 0.

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