Measure-geometric Laplacians for discrete distributions

Abstract

In 2002 Freiberg and Zähle introduced and developed a harmonic calculus for measure-geometric Laplacians associated to continuous distributions. We show their theory can be extended to encompass distributions with finite support and give a matrix representation for the resulting operators. In the case of a uniform discrete distribution we make use of this matrix representation to explicitly determine the eigenvalues and the eigenfunctions of the associated Laplacian.

8 pages, 4 figures

References in corpus (3)

• A note on measure-geometric Laplacians
• Stochastic Heat Equations defined by Fractal Laplacians on Cantor-like Sets
• Generalised Krein-Feller operators and gap diffusions via transformations of measure spaces