The Hilbert Transform on a Smooth Closed Hypersurface

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Abstract

In this paper a condensed account is given of results connected to the Hilbert transform on the smooth boundary of a bounded domain in Euclidean space and some of its related concepts, such as Hardy spaces and the Cauchy integral, in a Clifford analysis context. Clifford analysis, also known as the theory of monogenic functions, is a multidimensional function theory, which is at the same time a generalization of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. It offers a framework which is particularly suited for the integrated treatment of higher dimensional phenomena, without having to rely on tensorial approaches.

Keywords

Hilbert transform , Hardy space , Cauchy integral
  • F. Brackx Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium.
  • H. De Schepper Clifford Research Group, Department of Mathematical Analysis, Faculty of Engineering, Ghent University, Galglaan 2, 9000 Gent, Belgium.
  • Pages: 83–106
  • Date Published: 2008-07-01
  • Vol. 10 No. 2 (2008): CUBO, A Mathematical Journal

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Published

2008-07-01

How to Cite

[1]
F. Brackx and H. De Schepper, “The Hilbert Transform on a Smooth Closed Hypersurface”, CUBO, vol. 10, no. 2, pp. 83–106, Jul. 2008.

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