TY - JOUR
T1 - Boundary value problems associated to a Hermitian Helmholtz equation
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Brackx, Fred
AU - De Schepper, Hennie
AU - Sommen, Frank
N1 - Funding Information:
Ricardo Abreu Blaya and Juan Bory Reyes wish to thank all members of the Department of Mathematical Analysis of Ghent University, where the paper was written, for the invitation and hospitality. They were supported respectively by the Research Council of Ghent University and by the Research Foundation – Flanders (FWO, project 31506208).
PY - 2012/5/15
Y1 - 2012/5/15
N2 - As is the case for the Laplace operator, in Euclidean Clifford analysis also the Helmholtz operator can be factorized, more precisely by using perturbed Dirac operators. In this paper we consider the Helmholtz equation in a circulant matrix form in the context of Hermitian Clifford analysis. The aim is to introduce and study the corresponding inhomogeneous Hermitian Dirac operators, which will constitute a splitting of the traditional perturbed Dirac operators of the Euclidean Clifford analysis context. This will not only lead to special solutions of the Hermitian Helmholtz equation as such, but also to the study of boundary value problems of Riemann type for those solutions, which are, in fact, solutions of the Hermitian perturbed Dirac operators involved.
AB - As is the case for the Laplace operator, in Euclidean Clifford analysis also the Helmholtz operator can be factorized, more precisely by using perturbed Dirac operators. In this paper we consider the Helmholtz equation in a circulant matrix form in the context of Hermitian Clifford analysis. The aim is to introduce and study the corresponding inhomogeneous Hermitian Dirac operators, which will constitute a splitting of the traditional perturbed Dirac operators of the Euclidean Clifford analysis context. This will not only lead to special solutions of the Hermitian Helmholtz equation as such, but also to the study of boundary value problems of Riemann type for those solutions, which are, in fact, solutions of the Hermitian perturbed Dirac operators involved.
KW - Boundary value problems
KW - Helmholtz equations
KW - Hermitian Clifford analysis
UR - http://www.scopus.com/inward/record.url?scp=84856275073&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2012.01.006
DO - 10.1016/j.jmaa.2012.01.006
M3 - Artículo
SN - 0022-247X
VL - 389
SP - 1268
EP - 1279
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -