The absolutely continuous spectrum of Jacobi matrices
نویسندگان
چکیده
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...
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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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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2011
ISSN: 0003-486X
DOI: 10.4007/annals.2011.174.1.4