Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials


Journal Article

We prove that for any one-dimensional Schrödinger operator with potential V(x) satisfying decay condition |V(x)| ≦ Cx-3/4-ε, the absolutely continuous spectrum fills the whole positive semi-axis. The description of the set in ℝ+ on which the singular part of the spectral measure might be supported is also given. Analogous results hold for Jacobi matrices.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A

Published Date

  • January 1, 1996

Published In

Volume / Issue

  • 179 / 2

Start / End Page

  • 377 - 399

International Standard Serial Number (ISSN)

  • 0010-3616

Digital Object Identifier (DOI)

  • 10.1007/bf02102594

Citation Source

  • Scopus