Publications [#330332] of Alexander A. Kiselev

Papers Published

1. Kiselev, A, Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials, Communications in Mathematical Physics, vol. 179 no. 2 (January, 1996), pp. 377-399, Springer Nature [doi]
   (last updated on 2025/01/30)

   Abstract:
   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.