Local Spectral Properties of Reflectionless Jacobi, Cmv, and Schrödinger Operators
نویسندگان
چکیده
We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.
منابع مشابه
Essential Closures and Ac Spectra for Reflectionless Cmv, Jacobi, and Schrödinger Operators Revisited
We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application of the notion of the essential closure of subsets of R we revisit the fact that CMV, Jacobi, and Schrödinger operators, reflectionless on a set E of positiv...
متن کاملar X iv : 0 80 3 . 31 77 v 2 [ m at h . SP ] 1 5 M ay 2 00 8 LOCAL SPECTRAL PROPERTIES OF REFLECTIONLESS JACOBI , CMV , AND SCHRÖDINGER OPERATORS
We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.
متن کاملThe Absolutely Continuous Spectrum of One-dimensional Schrödinger Operators
This paper deals with general structural properties of one-dimensional Schrödinger operators with some absolutely continuous spectrum. The basic result says that the ω limit points of the potential under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure. This implies an Oracle Theorem for such potentials and DenisovRakhmanov type theorems....
متن کاملSpectral Properties of a Class of Reflectionless Schrödinger Operators
We prove that one-dimensional reflectionless Schrödinger operators with spectrum a homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and Yuditskii, have purely absolutely continuous spectra. This class includes all earlier examples of reflectionless almost periodic Schrödinger operators. In addition, we construct examples of reflectionless Schrödinger operator...
متن کاملEquality of the Spectral and Dynamical Definitions of Reflection
For full-line Jacobi matrices, Schrödinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of m-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x = −∞ as t → −∞ goes entirely to x = ∞ as t → ∞. This allows us to settle a conjecture of Deift and Simon from 1983 regarding erg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008