Publications [#330319] of Alexander A. Kiselev

Papers Published

1. Christ, M; Kiselev, A, WKB and spectral analysis of one-dimensional Schrödinger operators with slowly varying potentials, Communications in Mathematical Physics, vol. 218 no. 2 (January, 2001), pp. 245-262, Springer Nature [doi]
   (last updated on 2025/01/30)

   Abstract:
   Consider a Schrödinger operator on L2 of the line, or of a half line with appropriate boundary conditions. If the potential tends to zero and is a finite sum of terms, each of which has a derivative of some order in L1 + Lp for some exponent p < 2, then an essential support of the the absolutely continuous spectrum equals ℝ+. Almost every generalized eigenfunction is bounded, and satisfies certain WKB-type asymptotics at infinity. If moreover these derivatives belong to Lp with respect to a weight |x|γ with γ > 0, then the Hausdorff dimension of the singular component of the spectral measure is strictly less than one.