منابع مشابه
The absolutely continuous spectrum of Jacobi matrices
I explore some consequences of a groundbreaking result of Breimesser and Pearson on the absolutely continuous spectrum of one-dimensional Schrödinger operators. These include an Oracle Theorem that predicts the potential and rather general results on the approach to certain limit potentials. In particular, we prove a Denisov-Rakhmanov type theorem for the general finite gap case. The main theme...
متن کاملAbsolutely Continuous Spectrum of One-dimensional Schrr Odinger Operators and Jacobi Matrices with Slowly Decreasing Potentials
We prove that for any one-dimensional Schrr odinger operator with potential V (x) satisfying decay condition jV (x)j C x ?3=4? ; the absolutely continuous spectrum lls 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.
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CONTINUOUS SPECTRA. II BY C. R. PUTNAM Communicated by Maurice Heins, November 1, 1967 1. This paper is a continuation of [4]. It may be recalled that if A is a self-adjoint operator on a Hubert space § with spectral resolution A=zf\dE\, then the set of elements x in § for which ||-Ex#|| is an absolutely continuous function of X is a subspace, &a(A), of § (see, e.g., Halmos [l, p. 104]). The op...
متن کاملAbsolutely Continuous Spectrum of Perturbed Stark Operators
In this paper, we study the stability of the absolutely continuous spectrum of onedimensional Stark operators under various classes of perturbations. Stark Schrödinger operators describe behavior of the charged particle in the constant electric field. The absolutely continuous spectrum is a manifestation of the fact that the particle described by the operator propagates to infinity at a rather ...
متن کاملAbsolutely Continuous Spectrum of Stark Operators
Abstract. We prove several new results on the absolutely continuous spectrum of perturbed one-dimensional Stark operators. First, we find new classes of potentials, characterized mainly by smoothness condition, which preserve purely absolutely continuous spectrum. Then we establish stability of the absolutely continuous spectrum in more general situations, where imbedded singular spectrum may o...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2002
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-02-06339-6