The Hilbert Transform on a Smooth Closed Hypersurface
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F. Brackx
fb@cage.ugent.be
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H. De Schepper
fb@cage.ugent.be
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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.
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