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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 2, 1999, pp. 379–391
DOI: 10.4171/ZAA/888

Published online: 1999-06-30

Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis

Swanhild Bernstein[1]

(1) Technische Universität Bergakademie Freiberg, Germany

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 $C \mathcal l_{n, 0}$. 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

Bernstein Swanhild: Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis. Z. Anal. Anwend. 18 (1999), 379-391. doi: 10.4171/ZAA/888