Publications [#330320] of Alexander A. Kiselev

Papers Published

1. Christ, M; Kiselev, A, WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials, Journal of Functional Analysis, vol. 179 no. 2 (February, 2001), pp. 426-447, Elsevier BV [doi]
   (last updated on 2025/01/30)

   Abstract:
   We prove the WKB asymptotic behavior of solutions of the differential equation -d2u/dx2+V(x)u=Eu for a.e. E>A where V=V1+V2, V1∈Lp(R), and V2 is bounded from above with A=limsupx→∞V(x), while V′2(x)∈Lp(R), 1≤p<2. These results imply that Schrödinger operators with such potentials have absolutely continuous spectrum on (A, ∞). We also establish WKB asymptotic behavior of solutions for some energy-dependent potentials. © 2001 Academic Press.