Szego via Jacobi

被引：28

作者：

Boettcher, Albrecht ^{[1
]}

Widom, Harold

机构：

[1] TU Chemnitz, Fak Math, D-09107 Chemnitz, Germany

[2] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2006年 / 419卷 / 2-3期

基金：

美国国家科学基金会;

关键词：

Toeplitz determinant; strong Szego limit theorem; Borodin-Okounkov formula; nonvanishing index; Jacobi's theorem;

D O I：

10.1016/j.laa.2006.06.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

At present there exist numerous different approaches to results on Toeplitz determinants of the type of Szego's strong limit theorem. The intention of this paper is to show that Jacobi's theorem on the minors of the inverse matrix remains one of the most comfortable tools for tackling the matter. We repeat a known proof of the Borodin-Okounkov formula and thus of the strong Szego limit theorem that is based on Jacobi's theorem. We then use Jacobi's theorem to derive exact and asymptotic formulas for Toeplitz determinants generated by functions with nonzero winding number. This derivation is new and completely elementary. (c) 2006 Elsevier Inc. All rights reserved.

引用

页码：656 / 667

页数：12

共 21 条

[1]

[Anonymous], 2005, AMS C PUBLICATIONS

[2] On a Toeplitz determinant identity of Borodin and Okounkov [J].