Ehrhardt, Torsten; Shao, Bin Asymptotic behavior of variable-coefficient Toeplitz determinants. (English) Zbl 0990.47024 J. Fourier Anal. Appl. 7, No. 1, 71-92 (2001). Let \(\sigma\) be a continuous function on \([0,1]\times {\mathbb T}\), where \(\mathbb T\) is the unit circle. Denote by \(op_n \sigma\) the \((n+1)\times (n+1)\) matrix whose \((j,k)\)-entris are given by \({1 \over 2\pi} \int_0^{2\pi} \sigma ({j\over n}, e^{-i(j-k)\theta}) d\theta\). These matrices can be thought of as variable-coefficient Toeplitz matrices or as the discrete analogues of pseudodifferential operators. For functions \(\sigma\) with sufficiently smooth logarithms the authors establish the following asymptotic formula \(\det [op_n \sigma] \sim G[\sigma]^{(n+1)} E[\sigma]\), as \(n \rightarrow \infty\). The constants \(G[\sigma]\) and \(E[\sigma]\) are explicitly determined. Reviewer: Nikolaj L.Vasilevskij (México) Cited in 7 Documents MSC: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 15A15 Determinants, permanents, traces, other special matrix functions Keywords:Toeplitz determinant; Szegő limit theorem PDFBibTeX XMLCite \textit{T. Ehrhardt} and \textit{B. Shao}, J. Fourier Anal. Appl. 7, No. 1, 71--92 (2001; Zbl 0990.47024) Full Text: EuDML