TY - JOUR

T1 - A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials

AU - Deift, Percy

AU - Östensson, Jörgen

N1 - Funding Information:
The work of the first author was supported in part by the NSF Grant DMS-0296084. The second author would like to express his gratitude to the Wenner-Gren Foundations for their financial support. He is also grateful for the hospitality and stimulating environment provided by the Courant Institute. Both authors would like to thank Barry Simon for fruitful discussions.

PY - 2006/3

Y1 - 2006/3

N2 - In this paper, the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUCs). There are four main results: the first concerns the approximation of the inverse of a Toeplitz operator by the inverses of its finite truncations. The second concerns a new proof of the 'hard' part of Baxter's theorem, and the third concerns the Born approximation for a scattering problem on the lattice Z+. The fourth and final result concerns a basic proposition of Golinskii-Ibragimov arising in their analysis of the Strong Szegö Limit Theorem.

AB - In this paper, the authors show how to use Riemann-Hilbert techniques to prove various results, some old, some new, in the theory of Toeplitz operators and orthogonal polynomials on the unit circle (OPUCs). There are four main results: the first concerns the approximation of the inverse of a Toeplitz operator by the inverses of its finite truncations. The second concerns a new proof of the 'hard' part of Baxter's theorem, and the third concerns the Born approximation for a scattering problem on the lattice Z+. The fourth and final result concerns a basic proposition of Golinskii-Ibragimov arising in their analysis of the Strong Szegö Limit Theorem.

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U2 - 10.1016/j.jat.2005.08.001

DO - 10.1016/j.jat.2005.08.001

M3 - Article

AN - SCOPUS:33645859583

SN - 0021-9045

VL - 139

SP - 144

EP - 171

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

IS - 1-2

ER -