Toeplitz Determinants with Perturbations in the Corners

Authors

Albrecht Böttcher, Technische Universitat Chemnitz
Lenny Fukshansky, Claremont McKenna CollegeFollow
Stephan Ramon Garcia, Pomona CollegeFollow
Hiren Maharaj, Pomona College

Document Type

Article - postprint

Department

Mathematics (CMC), Mathematics (Pomona)

Publication Date

2015

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.

Rights Information

© 2014 Elsevier Inc.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

http://dx.doi.org/10.1016/j.jfa.2014.10.023

Recommended Citation

Boettcher, A., Fukshansky, L., Garcia, S., Maharaj, H. Toeplitz determinants with perturbations in the corners, Journal of Functional Analysis, vol. 268 no. 1 (2015), pg. 171--193.