Absolutely continuous spectrum of a one-paramentric family of\n Schr "odinger operators

2011/06/09 by Oleg Safronov, Safronov, Oleg
Mathematics · #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems #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.1106.1712

openalex publication_date 2011/06/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We consider a family of operators -\Δ+ t V with a slowly decaying and\noscillating potential V. We prove that the absolutely continuous spectrum of\nthis operator is essentially supported by [0,\∞) for almost every t.\n

Related

• Absolutely continuous spectrum of a typical Schrödinger operator with a slowly decaying potential
• Absolutely continuous spectrum for one-dimensional Schr "odinger\n operators with slowly decaying potentials: some optimal results
• Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators
• The absolutely continuous spectrum of Jacobi matrices
• Absolute continuity of the spectrum of a Schrodinger operator with a potential which is periodic in some directions and decays in others