Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials

2023/09/21 by Søren Mikkelsen, Mikkelsen, Søren · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2309.12015

openalex publication_date 2023/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider semiclassical Schrödinger operators acting in L²(ℝ^d) with d≥3. For these operators we establish a sharp spectral asymptotics without full regularity. For the counting function we assume the potential is locally integrable and that the negative part of the potential minus a constant is one time differentiable and the derivative is Hölder continues with parameter μ≥1/2. Moreover we also consider sharp Riesz means of order γ with γ∈(0,1]. Here we assume the potential is locally integrable and that the negative part of the potential minus a constant is two time differentiable and the second derivative is Hölder continues with parameter μ that depends on γ.

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