Spectral gaps of Schrödinger operators with periodic singular potentials

2009/03/30 by Plamen Djakov, Djakov, Plamen, Boris Mityagin +1 · 3 citations
Mathematics · Physics and Astronomy · #34B30 #34L40 #47E05 #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena

paper · doi:10.48550/arxiv.0903.5210

openalex publication_date 2009/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of one dimensional Schrödinger operators with periodic singular potentials v. Our results reveal a close relationship between smoothness of potentials and spectral gap asymptotics under a priori assumption v ∈ H^-1_loc (ℝ). They extend and strengthen similar results proved in the classical case v ∈ L²_loc(ℝ).

Cited by

• Asymptotic formulas for spectral gaps and deviations of Hill and 1D Dirac operators
• A generalized Birman-Schwinger principle and applications to one-dimensional Schrödinger operators with distributional potentials
• Perturbations of self-adjoint and normal operators with discrete spectrum

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