Integration over non-rectifiable curves and Riemann boundary value problems
type: Item
instance of: scholarly article
title: Integration over non-rectifiable curves and Riemann boundary value problems
zbMATH Open document ID: 1218.30104
author: Ricardo Abreu-Blaya
author: Juan Bory-Reyes
author: Boris A. Kats
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-05-10T00:00:00Z
review text: The authors introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. As an application, solvability conditions for the Riemann boundary value problem are derived under very weak conditions on the boundary. Under some natural assumptions, it is proved that the picture of solvability of this problem coincides with the classical case. The case of complex-valued functions is extended to the case of functions with values in Douglis algebras.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 30E25
zbMATH DE Number: 5886406
zbMATH Keywords: non-rectifiable curve
zbMATH Keywords: fractional dimension
zbMATH Keywords: Cauchy integral
zbMATH Keywords: Douglis algebra
zbMATH Keywords: Riemann boundary value problem
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.02.068
OpenAlex ID: W2068980588
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DOI: 10.1016/J.JMAA.2011.02.068
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description: scientific article; zbMATH DE number 5886406