Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials

Published

Journal Article

We show that when a potential bn of a discrete Schrödinger operator, defined on l2(Z{double-struck}+), slowly oscillates satisfying the conditions bn ∈ l∞ and ∂bn = bn+1 - bn ∈ lp, p < 2, then all solutions of the equation Ju = Eu are bounded near infinity at almost every E ∈ [-2 + lim supn→∞ bn, 2 + lim supn→∞ bn] ∩ [-2 + lim infn→∞bn, 2 + lim infn→∞bn]. We derive an asymptotic formula for generalized eigenfunctions in this case. As a corollary, the absolutely continuous spectrum of the corresponding Jacobi operator is essentially supported on the same interval of E. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Full Text

Duke Authors

Cited Authors

  • Kim, A; Kiselev, A

Published Date

  • April 1, 2009

Published In

Volume / Issue

  • 282 / 4

Start / End Page

  • 552 - 568

Electronic International Standard Serial Number (EISSN)

  • 1522-2616

International Standard Serial Number (ISSN)

  • 0025-584X

Digital Object Identifier (DOI)

  • 10.1002/mana.200810754

Citation Source

  • Scopus