The heat kernel of a Schrodinger operator with inverse square potential

作者：Ishige Kazuhiro^*; Kabeya Yoshitsugu; Ouhabaz El Maati

来源：Proceedings of the London Mathematical Society, 2017, 115(2): 381-410.

DOI：10.1112/plms.12041

• 35J10
• 47E05
• 35J08 (primary)

We consider the Schrodinger operator H=-+V(|x|) with radial potential V which may have singularity at 0 and a quadratic decay at infinity. First, we study the structure of positive harmonic functions of H and give their precise behavior. Second, under quite general conditions we prove an upper bound for the correspond heat kernel p(x,y,t) of the type 00, where U is a positive harmonic function of H. Third, if U2 is an A2 weight on RN, then we prove a lower bound of a similar type.

• 出版日期2017-8