Ultracontractivity and Functional Inequalities on Infinite Graphs
| Autor: | Shuang Liu, Hongye Song, Yong Lin |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
050101 languages & linguistics
Pure mathematics Property (philosophy) Inequality Semigroup media_common.quotation_subject 05 social sciences 02 engineering and technology Mathematics::Spectral Theory Curvature Theoretical Computer Science Sobolev inequality Combinatorics Computational Theory and Mathematics Volume growth 0202 electrical engineering electronic engineering information engineering Discrete Mathematics and Combinatorics 020201 artificial intelligence & image processing 0501 psychology and cognitive sciences Geometry and Topology Equivalence (measure theory) media_common Mathematics |
| Zdroj: | Discrete & Computational Geometry. 61:198-211 |
| ISSN: | 1432-0444 0179-5376 |
| DOI: | 10.1007/s00454-018-0014-0 |
| Popis: | We prove the equivalence between some functional inequalities and the ultracontractivity property of the heat semigroup on infinite graphs. These functional inequalities include Sobolev inequalities, Nash inequalities, Faber–Krahn inequalities, and log-Sobolev inequalities. We also show that, under the assumptions of volume growth and CDE(n, 0), which is regarded as the natural notion of curvature on graphs, these four functional inequalities and the ultracontractivity property of the heat semigroup are all true on graphs. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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