Discrete Clifford analysis: further development of the function theory and corresponding boundary value problems.

01 October 2013 → 30 August 2017
Regional and community funding: Special Research Fund, Research Foundation - Flanders (FWO)
Research disciplines
  • Natural sciences
    • Analysis
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