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Toeplitz determinants with one Fisher-Hartwig singularity. (English) Zbl 0909.47019
The authors study the asymptotic behaviour of the Toeplitz determinants \(T_n (c)\) as \(n\) tends to infinity in the case of symbols with one singularity. This symbol has a form \[ c(e^{i\theta} e^{i\theta}) \prod_{r}^R t_{\beta _r}\left( e^{i(\theta-i\theta _r)}\right) u_{\alpha _r}\left( e^{i(\theta-i\theta _r)}\right) \] where \(t_\beta \left (e^{i\theta} \right) ^{i\beta(\theta - \pi)}\), \(u_{\alpha}\left(e^{i\theta} \right)( 2- 2 \cos \theta)^\alpha\) and \(b\) are sufficiently smooth nonvanishing functions.

MSC:
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
15A15 Determinants, permanents, traces, other special matrix functions
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