Self-adjointness of Cauchy Singular Integral Operator

نویسنده

  • ALEXEY TIKHONOV
چکیده

We extend Krupnik’s criterion of self-adjointness of the Cauchy singular integral operator to the case of finitely connected domains. The main aim of the paper is to present a new approach for proof of the criterion. Let G+ be a finitely connected domain bounded by the rectifiable curve C = ∂G+, G− = C \ clos G+ and ∞ ∈ G−. Suppose also that w(z), z ∈ C is a nonnegative weight such that w(z) 6≡ 0 on each connected component of the curve C. For any f ∈ L(C, |dz|) , we denote by f±(z) , z ∈ C the angular boundary values of the Cauchy transform

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تاریخ انتشار 2005