Hyperbolic Function Theory in the Clifford Algebra {mathcal {C}}ell_{n+1, 0} |
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Authors: | Sirkka-Liisa Eriksson Heikki Orelma |
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Affiliation: | (1) Department of Mathematics, Tampere University of Technology, P.O. Box 527, FI-33101 Tampere, Finland |
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Abstract: | The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on . Received: October, 2007. Accepted: February, 2008. |
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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000). Primary 30G35 Secondary 30A05 |
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