JournalszaaVol. 18, No. 2pp. 379–391

Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis

  • Swanhild Bernstein

    Technische Universität Bergakademie Freiberg, Germany
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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 Cln,0C \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.

Cite this article

Swanhild Bernstein, Nonlinear Singular Integral Equations Involving the Hilbert Transform in Clifford Analysis. Z. Anal. Anwend. 18 (1999), no. 2, pp. 379–391

DOI 10.4171/ZAA/888