| 无界拉普拉斯算子下图上的泛函不等式 |
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| 引用本文： | 公超,林勇. 无界拉普拉斯算子下图上的泛函不等式[J]. 数学学报, 2018, 61(3): 503-510 |
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| 作者姓名： | 公超 林勇 |
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| 作者单位： | 中国人民大学信息学院 北京 100872 |
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| 摘 要： | 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.
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Functional Inequalities on Graph with Unbounded Laplacians |
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| Chao GONG,Yong LIN. Functional Inequalities on Graph with Unbounded Laplacians[J]. Acta Mathematica Sinica, 2018, 61(3): 503-510 |
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| Authors: | Chao GONG Yong LIN |
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| Affiliation: | Information School, Renmin University of China, Beijing 100872, P. R. China |
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| Abstract: | 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. |
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| Keywords: | unbounded Laplacian log-Sobolev inequality Nash inequality |
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