TY - JOUR
T1 - On the measure of the absolutely continuous spectrum for Jacobi matrices
AU - Shamis, Mira
AU - Sodin, Sasha
N1 - Funding Information:
The first author is supported in part by The Israel Science Foundation (Grant No. 1169/06 ) and by Grant 2006483 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel . The second author is supported in part by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and by the ISF .
PY - 2011/4
Y1 - 2011/4
N2 - We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support σac of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure of σac which takes into account the value distribution of the diagonal elements, and implies the bound due to Deift-Simon and Poltoratski-Remling.Second, we generalise the differential inequality of Deift-Simon for the integrated density of states associated with the absolutely continuous spectrum to general Jacobi matrices.
AB - We apply the methods of classical approximation theory (extreme properties of polynomials) to study the essential support σac of the absolutely continuous spectrum of Jacobi matrices. First, we prove an upper bound on the measure of σac which takes into account the value distribution of the diagonal elements, and implies the bound due to Deift-Simon and Poltoratski-Remling.Second, we generalise the differential inequality of Deift-Simon for the integrated density of states associated with the absolutely continuous spectrum to general Jacobi matrices.
KW - Absolutely continuous spectrum
KW - Chebyshev alternation theorem
KW - Density of states
KW - Jacobi matrices
UR - http://www.scopus.com/inward/record.url?scp=79952193358&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2010.12.003
DO - 10.1016/j.jat.2010.12.003
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AN - SCOPUS:79952193358
SN - 0021-9045
VL - 163
SP - 491
EP - 504
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
IS - 4
ER -