Toeplitz determinants with perturbations in the corners
Functional Analysis
2014-07-22 v2
Abstract
The paper is devoted to exact and asymptotic formulas for the determinants of Toeplitz matrices with perturbations by blocks of fixed size in the four corners. If the norms of the inverses of the unperturbed matrices remain bounded as the matrix dimension goes to infinity, then standard perturbation theory yields asymptotic expressions for the perturbed determinants. This premise is not satisfied for matrices generated by so-called Fisher-Hartwig symbols. In that case we establish formulas for pure single Fisher-Hartwig singularities and for Hermitian matrices induced by general Fisher-Hartwig symbols.
Cite
@article{arxiv.1406.7594,
title = {Toeplitz determinants with perturbations in the corners},
author = {Albrecht Boettcher and Lenny Fukshansky and Stephan Ramon Garcia and Hiren Maharaj},
journal= {arXiv preprint arXiv:1406.7594},
year = {2014}
}
Comments
20 pages