JournalsjstVol. 10, No. 1pp. 115–145

An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs

  • H. Daniel Lenz

    Friedrich-Schiller-Universität Jena, Germany

  • Peter Stollmann

    Technische Universität Chemnitz, Germany

  • Günter Stolz

    University of Alabama at Birmingham, USA
An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs cover
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Abstract

We prove a quantitative uncertainty principle at low energies for the Laplacian on fairly general weighted graphs with a uniform explicit control of the constants in terms of geometric quantities. A major step consists in establishing lower bounds for Dirichlet eigenvalues in terms of the geometry.

Cite this article

H. Daniel Lenz, Peter Stollmann, Günter Stolz, An uncertainty principle and lower bounds for the Dirichlet Laplacian on graphs. J. Spectr. Theory 10 (2020), no. 1, pp. 115–145

DOI 10.4171/JST/287