Bethe-Sommerfeld conjecture for pseudodifferential perturbation

2008/04/22 by Gerassimos Barbatis, Barbatis, G., Leonid Parnovski +1
Computer Science · Mathematics · Physics and Astronomy · #35J10 (Secondary) #35P20 (Primary) #58J40 #58J50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0804.3488

openalex publication_date 2008/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a periodic pseudodifferential operator H=(-Δ)^l+A (l>0) in \R^d which satisfies the following conditions: (i) the symbol of H is smooth in x, and (ii) the perturbation A has order smaller than 2l-1. Under these assumptions, we prove that the spectrum of H contains a half-line.

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