Some properties of the Clifford Cauchy type integrals associated to Helmholtz equation on a piecewise Lyapunov surfaces in \(\mathbb R^m\)
type: Item
instance of: scholarly article
title: Some properties of the Clifford Cauchy type integrals associated to Helmholtz equation on a piecewise Lyapunov surfaces in \(\mathbb R^m\)
zbMATH Open document ID: 1264.30040
author: Baruch Schneider
published in: Applied Mathematics and Computation
publication date: 2012-06-13T00:00:00Z
review text: Cauchy type integrals arising in relation with biquaternionic first-order differential operators factorizing the Helmholtz operator (in general with a biquaternionic wave number) were studied in a number of works (see [\textit{V. V. Kravchenko} and \textit{M. V. Shapiro}, Integral representations for spatial models of mathematical physics. Harlow: Longman (1996; Zbl 0872.35001); \textit{V. Kravchenko}, Applied quaternionic analysis. Lemgo: Heldermann Verlag (2003; Zbl 1014.78003)] and references therein). They found applications in studying time-harmonic electromagnetic fields, solutions of the Dirac equation, Beltrami and force-free magnetic fields. In several previous publications the author considered biquaternionic Cauchy-type integrals on piecewise Lyapunov surfaces (see [Appl. Math. E-Notes 7, 139--146 (2007; Zbl 1154.78301); with \textit{M. Shapiro}, Integral Equations Oper. Theory 44, No. 1, 93--126 (2002; Zbl 1020.30052)]). In the present paper he transfers several properties of such integrals to Clifford algebra valued functions.
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 6045824
zbMATH Keywords: Clifford analysis
zbMATH Keywords: Cauchy type integrals
MaRDI profile type: Publication
full work available at URL: j.amc.2011.09.057
OpenAlex ID: W2080213321
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DOI: 10.1016/J.AMC.2011.09.057
description: scientific article; zbMATH DE number 6045824