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 AnalysisS. BernsteinS. Bernstein: University of Mining and Technology, Inst. Appl. Math., D-09596 FreibergAbstract: 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 Full text of the article:
Electronic fulltext finalized on: 31 Jul 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
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