A property of the β-Cauchy-type integral with continuous density

R. Abreu Blaya, J. Bory Reyes

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Abstract

A theorem from the classical complex analysis proved by Davydov in 1949 is extended to the theory of solution of a special case of the Beltrami equation in the z-complex plane (i.e., null solutions of the differential operator equation is present. It is proved that if γ is a rectifiable Jordan closed curve and f is a continuous complex-valued function on γ such that the integral equation is present converges uniformly on γ as r∈→∈0, where n(ζ) is the unit vector of outer normal on γ at a point ζ and ds is the differential of arc length, then the β-Cauchy-type integral equation is present admits a continuous extension to γ and a version of the Sokhotski-Plemelj formulas holds. © 2008 Springer Science+Business Media, Inc.
Original languageAmerican English
Pages (from-to)1683-1690
Number of pages1513
JournalUkrainian Mathematical Journal
DOIs
StatePublished - 1 Nov 2008
Externally publishedYes

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