Measure-geometric Laplacians for discrete distributions

Marc Kesseböhmer, Tony Samuel, Hendrik Weyer

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.
Original languageEnglish
Title of host publicationHorizons of Fractal Geometry and Complex Dimensions
EditorsRobert G. Niemeyer, Erin P. J. Pearse, John A. Rock, Tony Samuel
PublisherAmerican Mathematical Society
Number of pages10
ISBN (Electronic)978-1-4704-5315-2
ISBN (Print)978-1-4704-3581-3
Publication statusPublished - 1 Jan 2019
Event2016 Summer School on Fractal Geometry and Complex Dimensions : In celebration of the 60th birthday of Michel Lapidus - California Polytechnic, San Luis Obispo, United States
Duration: 21 Jun 201629 Jun 2016

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627


Conference2016 Summer School on Fractal Geometry and Complex Dimensions
Country/TerritoryUnited States
CitySan Luis Obispo


  • Measure-geometric Laplacians
  • Spectral asymptotics


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