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:

scopusscopus

Tipo de documento:

Article

Estado:

Acceso restringido

Áreas de conocimiento:

  • Optimización matemática
  • Optimización matemática

Áreas temáticas:

  • Álgebra