EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 2, pp. 379 - 391 (1999)

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Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis

S. Bernstein

S. Bernstein: University of Mining and Technology, Inst. Appl. Math., D-09596 Freiberg

Abstract: We apply operator-theoretical methods for monotone and maximal monotone operators to prove the existence of solutions for nonlinear singular integral and integro-differential equations involving the Hilbert transform in the Clifford algebra $\Cl_{n,0}$. Properties of the Hilbert transform are proved using Clifford analysis. We generalize well-known results concerning the complex Hilbert transform and the singular Cauchy integral operator to higher dimensions.

Keywords: Clifford analysis, Cauchy-type integrals, nonlinear integro-differential equations

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Electronic fulltext finalized on: 31 Jul 2001. This page was last modified: 9 Nov 2001.

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