Communications in Mathematics and Statistics

, Volume 6, Issue 4, pp 493–508 | Cite as

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

  • Jian Wang


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.


Schrödinger semigroup (Dirichlet) heat kernel Intrinsic contractivity property Eigenvalue 

Mathematics Subject Classification

60G51 60G52 60J25 60J75 



The author is grateful to the referee for his/her corrections. The research is 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) and the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ).


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Copyright information

© School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and Informatics & Fujian Key Laboratory of Mathematical Analysis and ApplicationsFujian Normal UniversityFuzhouPeople’s Republic of China

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