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A matrix Hilbert transform in Hermitean Clifford analysisJournal of Mathematical Analysis and Applications, 344
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer
- Subject
- Mathematics; Theoretical, Mathematical and Computational Physics; Mathematics, general
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-009-0018-8
- Publisher site
- See Article on Publisher Site
Abstract
Euclidean Clifford analysis is a higher dimensional function theory, refining harmonic analysis, centred around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator, called the Dirac operator. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions of two Hermitean Dirac operators, invariant under the action of the unitary group. In this paper, a Cauchy integral formula is established by means of a matrix approach, allowing the recovering of the traditional Martinelli-Bochner formula for holomorphic functions of several complex variables as a special case.
Journal
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Sep 4, 2009