Schrödinger operators with singular Gordon potentials

Abstract

Singular Gordon potentials are defined to be distributions from the space W^{-1}_{2,unif}(R) that are sufficiently fast approximated by periodic ones. We prove that Schrödinger operators with singular Gordon potentials have no point spectrum and show that a rich class of quasiperiodic distributions consists of singular Gordon potentials.

13 pages, Amslatex, to appear in Meth. Funct. Anal. Topol

References in corpus (2)

• Schrödinger Operators with Periodic Singular Potentials
• A generalization of Gordon's theorem and applications to quasiperiodic Schrödinger operators

Cited by in corpus (5)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• Schrödinger Operators with Periodic Singular Potentials
• Spectral gaps of Schrödinger operators with periodic singular potentials
• Inverse spectral problems for Sturm-Liouville operators with singular potentials, II. Reconstruction by two spectra
• Equiconvergence of spectral decompositions of Hill-Schrödinger operators