96-2 Kiselev A.

Absolutely Continuous Spectrum of One-Dimensional Schr\"odinger Operators and Jacobi Matrices with Slowly Decreasing Potentials (71K, LaTeX) Jan 3, 96

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We prove that for any one-dimensional Schr\"odinger operator with potential $V(x)$ satisfying decay condition $|V(x)| \leq Cx^{-3/4-\epsilon},$ 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.

Files: 96-2.tex