TY - JOUR
T1 - Matrix Cauchy and Hilbert transforms in Hermitian quaternionic Clifford analysis
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Brackx, Fred
AU - De Schepper, Hennie
AU - Sommen, Frank
N1 - Funding Information:
This article was written during a scientific stay of R. Abreu-Blaya at the Clifford Research Group of the Department of Mathematical Analysis of Ghent University, supported by a grant of the research council of Ghent University (BOF). He wishes to thank the members of the Clifford Research Group for their kind hospitality during this stay.
PY - 2013/8
Y1 - 2013/8
N2 - 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.
AB - 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.
KW - Cauchy integral
KW - Hilbert transform
KW - quaternionic Hermitian Clifford analysis
UR - http://www.scopus.com/inward/record.url?scp=84882644371&partnerID=8YFLogxK
U2 - 10.1080/17476933.2011.626034
DO - 10.1080/17476933.2011.626034
M3 - Artículo
SN - 1747-6933
VL - 58
SP - 1057
EP - 1069
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 8
ER -