کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6419296 | 1339390 | 2012 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Boundary value problems associated to a Hermitian Helmholtz equation Boundary value problems associated to a Hermitian Helmholtz equation](/preview/png/6419296.png)
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.
Journal: Journal of Mathematical Analysis and Applications - Volume 389, Issue 2, 15 May 2012, Pages 1268-1279