HEAT KERNELS OF METRIC TREES AND APPLICATIONS

被引：6
作者：
Frank, Rupert L. [1 ]
Kovarik, Hynek [2 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[2] Univ Brescia, Dipartimento Matemat, I-25123 Brescia, Italy
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 03期
关键词：
heat kernel; metric tree; eigenvalue estimate; Sobolev inequality; SCHRODINGER-OPERATORS; INEQUALITIES; EIGENVALUES; HARDY; ROZENBLUM;
D O I：
10.1137/120886297
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the heat semigroup generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schrodinger operators on metric trees.
引用
收藏
页码：1027 / 1046
页数：20
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