TWO-SIDED HEAT KERNEL ESTIMATES FOR SCHRÖDINGER OPERATORS WITH UNBOUNDED POTENTIALS

• 成果类型: Article
• 署名作者: Chen, Xin; Wang, Jian
• 署名单位: Shanghai Jiao Tong University; Fujian Normal University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1680
• 发表日期: 2024
• 页码: 1016-1047
• 关键词: feynman-kac semigroups; schrodinger operator; intrinsic ultracontractivity; bounds; compactness; BEHAVIOR

摘要

Consider the Schrodinger operator L-V = - Delta + V on R-d , where V : R-d -> [0 , infinity) is a nonnegative and locally bounded potential on R-d so that for all x is an element of R-d with | x | >= 1, c(1)g( | x | ) <= V (x) <= c(2)g( | x | ) with some constants c 1 , c(2) > 0 and a nondecreasing and strictly positive function g : [0,infinity) -> [1 ,+infinity ) that satisfies g(2r) <= c(0)g(r) for all r > 0 and lim(r ->infinity )g(r) = infinity . We establish global in time and qualitatively sharp bounds for the heat kernel of the associated Schr delta dinger semigroup by the probabilistic method. In particular, we can present global in space and time two-sided bounds of heat kernel even when the Schrodinger semigroup is not intrinsically ultracontractive. Furthermore, two-sided estimates for the corresponding Green's function are also obtained.