Code
3E003913
Duration
01 October 2013 → 30 August 2017
Funding
Regional and community funding: Special Research Fund, Research Foundation - Flanders (FWO)
Promotor
Fellow
Research disciplines
-
Natural sciences
- Analysis
Keywords
discrete heatequation
Hilbert transformation
orthogonal bases
discrete clifford analysis
Project description
We further develop the theory of discrete monogenic functions; i.e. functions on the grid Z^m which are null-solutions of a discrete Dirac operator factorizing the discrete Laplacian. We focus on:
(1) constructing orthogonal bases for spaces of discrete spherical monogenics
(2) finding a suitable fundamental solution to the discrete Dirac operator
(3) the study of an explicit discrete Hilbert transform
(4) the determination of solutions of a discretized heat equation