Title

Finite Gap Jacobi Matrices, III. Beyond the Szego Class

Authors

Authors

J. S. Christiansen; B. Simon;M. Zinchenko

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Constr. Approx.

Keywords

Szego asymptotics; Orthogonal polynomials; Almost periodic sequences; Slowly decaying perturbations; PERTURBATIONS; BOUNDS; Mathematics

Abstract

Let e. R be a finite union of l + 1 disjoint closed intervals, and denote by omega(j) the harmonic measure of the j left- most bands. The frequency module for e is the set of all integral combinations of omega(1), ... , omega(l). Let {(a)over tilde (n), (b)over tilde (n)}(n=-8)(infinity) be a point in the isospectral torus for e and (p)over tilde(n) its orthogonal polynomials. Let {a(n), b(n)}(n=1)(infinity) be a half-line Jacobi matrix with a(n) = a(n) + delta(an), b(n) = (b)over tilde(n) + delta b(n). Suppose [GRAPHICS] and Sigma(n)(n=1) e(2 pi i omega N) delta a(n), Sigma(N)(n=1) e2pi.ndbn have finite limits as N -> 8 for all. in the frequency module. If, in addition, these partial sums grow at most subexponentially with respect to omega, then for z is an element of C \ R, p(n)(z)/(p) over tilde n(z) has a limit as n ->infinity. Moreover, we show that there are non-Szego class J's for which this holds.

Journal Title

Constructive Approximation

Volume

35

Issue/Number

2

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

259

Last Page

272

WOS Identifier

WOS:000300521500006

ISSN

0176-4276

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