supported by China Postdoctoral Science Foundation funded project(Grant No.201104383);the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56);National Natural Science Foundation of China(Grant No.10925106);Guangdong Province Key Laboratory of Computational Science and Grant for Senior Scholars from the Association of Colleges and Universities of Guangdong
Let (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2(X). Assume that the semigroup e-^tL gen...