Discrete convolution-rearrangement inequalities and the Faber-Krahn inequality on regular trees

DOI10.1215/S0012-7094-98-09119-0zbMath0943.05056OpenAlexW1515727144MaRDI QIDQ1974784

Alexander R. Pruss

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-98-09119-0

zbMATH Keywords

regular treesFaber-Krahn inequalityoctahedrondiscrete metric spacesline graphscircle graphsconvolution-rearrangement inequalities

Mathematics Subject Classification ID

Trees (05C05) Metric spaces, metrizability (54E35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Inequalities involving eigenvalues and eigenvectors (15A42)

Related Items

The first Dirichlet eigenvalue of bicyclic graphs, Explicit approximation of the symmetric rearrangement by polarizations, Faber-Krahn type inequalities for trees, Rearrangement inequalities in the discrete setting and some applications, Weighted join operators on directed trees, A decreasing rearrangement for functions on homogeneous trees, Symmetrization inequalities for difference equations on graphs, The parabolic Anderson model in a dynamic random environment: space-time ergodicity for the quenched Lyapunov exponent, Faber–Krahn type inequality for unicyclic graphs, On a New Class of Variational Problems

Cites Work

• Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
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• Symmetrization inequalities for difference equations on graphs
• Sharp bound of the \(k\)th eigenvalue of trees
• A Faber-Krahn-type inequality for regular trees
• A general rearrangement inequality for multiple integrals
• Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
• Three counterexamples for a question concerning Green’s functions and circular symmetrization
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