Article - preprint
Mathematics (Pomona), Mathematics (CMC)
Toeplitz matrix, Toeplitz determinant, Fisher-Hartwig symbol
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.
© 2015 Elsevier B.V.
Böttcher, A., Fukshansky, L., Garcia, S.R., Maharaj, H., Toeplitz determinants with perturbations in the corners, Journal of Functional Analysis 268 (2015), 171-193.