The heat kernel of a Schrödinger operator with inverse square potential
Language
en
Article de revue
This item was published in
Proceedings of the London Mathematical Society. 2017
London Mathematical Society
English Abstract
We consider the Schrödinger 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 ...Read more >
We consider the Schrödinger 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 0 < p(x, y, t) ≤ C t − N 2 U (min{|x|, √ t})U (min{|y|, √ t}) U (√ t) 2 exp − |x − y| 2 Ct for all x, y ∈ R N and t > 0, where U is a positive harmonic function of H. Third, if U 2 is an A 2 weight on R N , then we prove a lower bound of a similar type.Read less <
ANR Project
Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013
Origin
Hal imported