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⊂ C n. 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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