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, Clemson University

Document Type

Article - preprint

Department

Mathematics (Pomona), Mathematics (CMC)

Publication Date

2015

Keywords

Toeplitz matrix, Toeplitz determinant, Fisher-Hartwig symbol

Abstract

This 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 the Hermitian matrices induced by general Fisher-Hartwig symbols.

Comments

Final published version can be found at: Böttcher, A., Fukshansky, L., Garcia, S.R., Maharaj, H., Toeplitz determinants with perturbations in the corners, Journal of Functional Analysis 268 (2015), 171-193.

Rights Information

© 2015 Elsevier B.V.

DOI

10.1016/j.jfa.2014.10.023

Recommended Citation

Böttcher, A., Fukshansky, L., Garcia, S.R., Maharaj, H., Toeplitz determinants with perturbations in the corners, Journal of Functional Analysis 268 (2015), 171-193.