Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators

1996/10/01 by Alexander Kiselev, Kiselev, Alexander · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/9610216

openalex publication_date 1996/10/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and periodic Schrödinger operators is preserved under perturbations by all potentials V(x) satisfying |V(x)| ≤ C(1+x)^-(2)/(3)-ε. The main new technique includes an a.e. convergence theorem for a class of integral operators.

Cited by

• Absolutely continuous spectrum for one-dimensional Schr "odinger\n operators with slowly decaying potentials: some optimal results
• Absolutely continuous spectrum of perturbed Stark operators
• Stability of Spectral Types for Jacobi Matrices Under Decaying Random Perturbations

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