Universal inequalities for Dirichlet eigenvalues on discrete groups
Bobo Hua
Fudan University, Shanghai, P.R. ChinaAriel Yadin
Ben-Gurion University of the Negev, Be’er Sheva, Israel
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Abstract
We prove universal inequalities for Laplacian eigenvalues with Dirichlet boundary condition on subsets of certain discrete groups. The study of universal inequalities on Riemannian manifolds was initiated by Weyl, Pólya, Yau, and others. Here we focus on a version by Cheng and Yang. Specifically, we prove Yang-type universal inequalities for Cayley graphs of finitely generated amenable groups, as well as for the -regular tree (simple random walk on the free group).
Cite this article
Bobo Hua, Ariel Yadin, Universal inequalities for Dirichlet eigenvalues on discrete groups. J. Spectr. Theory 14 (2024), no. 3, pp. 933–957
DOI 10.4171/JST/498