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Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis.
- Source :
-
Complex Variables & Elliptic Equations . Aug2013, Vol. 58 Issue 8, p1057-1069. 13p. - Publication Year :
- 2013
-
Abstract
- Recently the basic setting has been established for the development of quaternionic Hermitian Clifford analysis, a theory centred around the simultaneous null solutions, calledq-Hermitian monogenic functions, of four Hermitian Dirac operators in a quaternionic Clifford algebra setting. Borel–Pompeiu and Cauchy integral formulae have been established in this framework by means of a (4 × 4) circulant matrix approach. By means of the matricial quaternionic Hermitian Cauchy kernel involved in these formulae, a quaternionic Hermitian Cauchy integral may be defined. The subsequent study of the boundary limits of this Cauchy integral then leads to the definition of a quaternionic Hermitian Hilbert transform. These integral transforms are studied in this article. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17476933
- Volume :
- 58
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Complex Variables & Elliptic Equations
- Publication Type :
- Academic Journal
- Accession number :
- 89686548
- Full Text :
- https://doi.org/10.1080/17476933.2011.626034