On lacunary Toeplitz determinants

Article type: Research Article

Authors: Kozlowski, K.K.

Affiliations: UMR 5584 du CNRS, Institut de Mathématiques de Bourgogne, Université de Bourgogne, France. E-mail: karol.kozlowski@u-bourgogne.fr

Abstract: By using Riemann–Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants det N[cℓa−mb[f]] generated by holomorphic symbols, where ℓa=a (resp. mb=b) except for a finite subset of indices a=h1,…,hn (resp. b=t1,…,tr). In addition to the usual Szegö asymptotics, our answer involves a determinant of size n+r.

Keywords: Toeplitz determinants, Toeplitz minors, large-size determinants

DOI: 10.3233/ASY-131210

Journal: Asymptotic Analysis, vol. 88, no. 1-2, pp. 1-16, 2014