Publications [#330298] of Alexander A. Kiselev

Papers Published

1. Kim, A; Kiselev, A, Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials, Mathematische Nachrichten, vol. 282 no. 4 (April, 2009), pp. 552-568, WILEY [doi]
   (last updated on 2025/01/30)

   Abstract:
   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.