Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure

Bobo Hua; Matthias Keller; Michael Schwarz; Melchior Wirth

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arXiv · 1804.08353

Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure

Bobo Hua·Matthias Keller·Michael Schwarz·Melchior Wirth

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Abstract

In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds can not be established.

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BibTeX RIS

Bobo Hua, Matthias Keller, Michael Schwarz, Melchior Wirth. 2018-04-23. Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure. https://arxiv.org/abs/1804.08353

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