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Asymptotic Formulas for Determinants of a Special Class of Toeplitz + Hankel Matrices

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 259))

Abstract

We compute the asymptotics of the determinants of certain n × n Toeplitz + Hankel matrices \( T_{n}(a)+Hn(b) \, {\rm as} \, n\rightarrow \infty \) with symbols of Fisher–Hartwig type. More specifically we consider the case where a has zeros and poles and where b is related to a in specific ways. Previous results of Deift, Its and Krasovsky dealt with the case where a is even. We are generalizing this in a mild way to certain non-even symbols.

Mathematics Subject Classification (2010). 47B35, 47A20, 15B52, 82B.

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Correspondence to Estelle Basor .

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Basor, E., Ehrhardt, T. (2017). Asymptotic Formulas for Determinants of a Special Class of Toeplitz + Hankel Matrices. In: Bini, D., Ehrhardt, T., Karlovich, A., Spitkovsky, I. (eds) Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications, vol 259. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49182-0_9

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