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Title: N{sup ±}-integrals and boundary values of Cauchy-type integrals of finite measures

Let Γ be a simple closed Lyapunov contour with finite complex measure ν, and let G{sup +} be the bounded and G{sup −} the unbounded domains with boundary Γ. Using new notions (so-called N-integration and N{sup +}- and N{sup −}-integrals), we prove that the Cauchy-type integrals F{sup +}(z), z∈G{sup +}, and F{sup −}(z), z∈G{sup −}, of ν are Cauchy N{sup +}- and N{sup −}-integrals, respectively. In the proof of the corresponding results, the additivity property and the validity of the change-of-variable formula for the N{sup +}- and N{sup −}-integrals play an essential role. Bibliography: 21 titles. (paper)
Authors:
 [1]
  1. Baku State University (Azerbaijan)
Publication Date:
OSTI Identifier:
22364929
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 7; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; COMPLEXES; INTEGRAL CALCULUS; INTEGRALS; LYAPUNOV METHOD; MATHEMATICAL SOLUTIONS