Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials

2024/01/17 by Xin Chen, Jian Wang, Chen, Xin +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2401.09005

openalex publication_date 2024/01/17 · openalex created_date 2024/01/19 · openalex updated_date 2026/07/28

Abstract

We establish global two-sided heat kernel estimates (for full time and space) of the Schrödinger operator -(1)/(2)Δ+V on \R^d, where the potential V(x) is locally bounded and behaves like c|x|^-α near infinity with α∈ (0,2) and c> 0, or with α>0 and c<0.Our results improve all known results in the literature, and it seems that the current paper is the first one where consistent two-sided heat kernel bounds for the long range potentials are established.

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