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PDF(408 KB)
PDF(408 KB)
无界拉普拉斯算子下图上的泛函不等式
Functional Inequalities on Graph with Unbounded Laplacians
本文探讨图上的泛函不等式，并且在无界拉普拉斯算子的意义下，利用图的完备性和图上超压缩性的性质，证明了图上对数Sobolev不等式的成立，以及超压缩性与图上Nash不等式的等价关系.
In this paper, we mainly talk about the functional inequalities on graph. With unbounded Laplacians, by use of the completeness and ultracontractivity, we prove the log-Sobolev inequality and that the ultracontractivity is equal to Nash inequality on graph.
无界拉普拉斯算子 / 对数Sobolev不等式 / Nash不等式 {{custom_keyword}} /
unbounded Laplacian / log-Sobolev inequality / Nash inequality {{custom_keyword}} /
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