Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis
Abstract:
Recently the basic setting has been established for the development of quaternionic Hermitian Clifford analysis, a theory centred around the simultaneous null solutions, called q-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. © 2013 Copyright Taylor and Francis Group, LLC.
Año de publicación:
2013
Keywords:
- Quaternionic Hermitian Clifford analysis
- Cauchy integral
- Hilbert Transform
Fuente:
Tipo de documento:
Article
Estado:
Acceso restringido
Áreas de conocimiento:
- Optimización matemática
- Optimización matemática
Áreas temáticas:
- Álgebra