@inproceedings{34120313e98443aab20cf7306f62d0c2,

title = "Measure-geometric Laplacians for discrete distributions",

abstract = "In 2002 Freiberg and Z{\"a}hle 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.",

keywords = "Measure-geometric Laplacians, Spectral asymptotics",

author = "Marc Kesseb{\"o}hmer and Tony Samuel and Hendrik Weyer",

year = "2019",

month = jan,

day = "1",

doi = "10.1090/conm/731/14676",

language = "English",

isbn = "978-1-4704-3581-3",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "133--142",

editor = "Niemeyer, {Robert G. } and Pearse, {Erin P. J. } and Rock, {John A. } and Samuel, {Tony }",

booktitle = "Horizons of Fractal Geometry and Complex Dimensions",

address = "United States",

note = "2016 Summer School on Fractal Geometry and Complex Dimensions : In celebration of the 60th birthday of Michel Lapidus ; Conference date: 21-06-2016 Through 29-06-2016",

}