Formulas for the inverses of Toeplitz matrices with polynomially singular symbols

被引：9

作者：

Rambour, P ^{[1
]}

Seghier, A ^{[1
]}

机构：

[1] Univ Paris 11, F-91405 Orsay, France

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2004年 / 50卷 / 01期

关键词：

Toeplitz matrix; singular symbol; entries of the inverse matrix; Green's function;

D O I：

10.1007/s00020-003-1298-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider large finite Toeplitz matrices with symbols of the form (1 - cos theta)(p) f (theta) where p is a natural number and f is a sufficiently smooth positive function. By employing techniques based on the use of predictor polynomials, we derive exact and asymptotic formulas for the entries of the inverses of these matrices. We show in particular that asymptotically the inverse matrix mimics the Green kernel of a boundary value problem for the differential operator (-1)p d(2p)/dx(2p).

引用

页码：83 / 114

页数：32