Semiclassical resolvent bound for compactly supported L^∞ potentials

2018/02/25 by Jacob Shapiro, Shapiro, Jacob
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1802.09008

openalex publication_date 2018/02/25 · openalex created_date 2018/03/06 · openalex updated_date 2026/07/28

Abstract

We give an elementary proof of a weighted resolvent estimate for semiclassical Schrödinger operators in dimension n ≥ 1. We require the potential belong to L^∞(ℝⁿ) and have compact support, but do not require that it have derivatives in L^∞(ℝⁿ). The weighted resolvent norm is bounded by e^Ch^-4/3log(h^-1), where h is the semiclassical parameter.

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