On-diagonal Heat Kernel Estimates for Schrödinger Semigroups and Their Application  

作　　者：Jian Wang 

机构地区：[1]College of Mathematics and Informatics&Fujian Key Laboratory of Mathematical Analysis and Applications,Fujian Normal University,350007 Fuzhou,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2018年第4期493-508,共16页数学与统计通讯（英文）

基　　金：supported by the National Natural Science Foundation of China(Nos.11522106 and 11831014);the Fok Ying Tung Education Foundation(No.151002);the Program for Probability and Statistics:Theory and Application(No.IRTL1704);the Program for Innovative Research Team in Science and Technology in Fujian Province University(IRTSTFJ).

摘　　要：We establish explicit and sharp on-diagonal heat kernel estimates for Schrödinger semigroups with unbounded potentials corresponding to a large class of symmetric jump processes.The approach is based on recent developments on the two-sided(Dirichlet)heat kernel estimates and intrinsic contractivity properties for symmetric jump processes.As a consequence,we present a more direct argument to yield asymptotic behaviors for eigenvalues of associated nonlocal operators.

关 键 词：Schrödinger semigroup (Dirichlet)heat kernel Intrinsic contractivity property Eigenvalue 

分 类 号：O17[理学—数学]