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Relative Szego Asymptotics for Toeplitz Determinants
Royal Inst Technol KTH, Dept Math, Stockholm Lindstedsvagen 25, SE-10044 Stockholm, Sweden.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2019 (English)In: International mathematics research notices, ISSN 1073-7928, E-ISSN 1687-0247, Vol. 2019, no 17, p. 5441-5496Article in journal (Refereed) Published
Abstract [en]

We study the asymptotic behaviour, as n -> infinity, of ratios of Toeplitz determinants D-n(e(h)d mu)/D-n(d mu) defined by a measure mu on the unit circle and a sufficiently smooth function h. The approach we follow is based on the theory of orthogonal polynomials. We prove that the second order asymptotics depends on h and only a few Verblunsky coefficients associated to mu. As a result, we establish a relative version of the Strong Szego Limit Theorem for a wide class of measures mu with essential support on a single arc. In particular, this allows the measure to have a singular component within or outside of the arc.

Place, publisher, year, edition, pages
OXFORD UNIV PRESS , 2019. Vol. 2019, no 17, p. 5441-5496
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-397296DOI: 10.1093/imrn/rnx266ISI: 000493555800007OAI: oai:DiVA.org:uu-397296DiVA, id: diva2:1375934
Funder
Swedish Research Council, 2012-3128Swedish Research Council, KAW 2010.0063Knut and Alice Wallenberg FoundationAvailable from: 2019-12-06 Created: 2019-12-06 Last updated: 2019-12-06Bibliographically approved

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Kozhan, Rostyslav

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