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arXiv · 1702.03873

Measure-geometric Laplacians for discrete distributions

Marc Kesseböhmer·Tony Samuel·Hendrik Weyer
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Abstract

In 2002 Freiberg and Z\"ahle 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.

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Marc Kesseböhmer, Tony Samuel, Hendrik Weyer. 2017-02-13. Measure-geometric Laplacians for discrete distributions. https://doi.org/10.14712/1213-7243.2020.026

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