Heat kernel estimates of fractional Schrödinger operators with negative hardy potential

2018/09/07 by Tomasz Jakubowski, Jian Wang, Jakubowski, Tomasz +1 · 1 citation
Mathematics · #Numerical methods in inverse problems #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1809.02425

Abstract

We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schrödinger operator with negative Hardy potential Δ^α/2 -λ|x|^-α on \RR^d, where α∈(0,d\wedge 2) and λ>0. The proof is purely analytical but elementary. In particular, for upper bounds of heat kernel we use the Chapman-Kolmogorov equation and adopt self-improving argument.

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• Two-sided weighted bounds on fundamental solution to fractional Schrödinger operator

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