A note on measure-geometric Laplacians

Marc Kesseböhmer, Tony Samuel, Hendrik Weyer

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We consider the measure-geometric Laplacians Δμ with respect to atomless compactly supported Borel probability measures μ as introduced by Freiberg and Zähle (Potential Anal. 16(1):265–277, 2002) and show that the harmonic calculus of Δμ can be deduced from the classical (weak) Laplacian. We explicitly calculate the eigenvalues and eigenfunctions of Δμ. Further, it is shown that there exists a measure-geometric Laplacian whose eigenfunctions are the Chebyshev polynomials and illustrate our results through specific examples of fractal measures, namely inhomogeneous self-similar Cantor measures and Salem measures.
Original languageEnglish
Pages (from-to)643-655
Number of pages12
JournalMonatshefte fur Mathematik
Issue number3
Early online date11 Apr 2016
Publication statusPublished - Nov 2016


  • Measure-geometric Laplacians
  • Spectral asymptotics
  • Singular measures
  • Chebyshev polynomials
  • Salem measures


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