|
|||||
|
|
On solutions of a discretized heat equation in discrete Clifford analysis |
|
| Authors: | F. Baaske S. Bernstein F. Sommen |
| Affiliation: | 1. Department of Mathematics, Friedrich-Schiller-University Jena, Jena, Germany;2. Fakult?t für Mathematik und Informatik, Institut für Angewandte Analysis, TU Bergakademie Freiberg, Freiberg, Germany;3. Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000, Gent, Belgium |
| Abstract: | The main purpose of this paper was to study solutions of the heat equation in the setting of discrete Clifford analysis. More precisely we consider this equation with discrete space and continuous time. Thereby we focus on representations of solutions by means of dual Taylor series expansions. Furthermore we develop a discrete convolution theory, apply it to the inhomogeneous heat equation and construct solutions for the related Cauchy problem by means of heat polynomials. |
| Keywords: | heat equation heat kernel discrete Clifford analysis |