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A status report on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities. (English) Zbl 0993.47028
Dijksma, A. (ed.) et al., Recent advances in operator theory. The Israel Gohberg anniversary volume. Proceedings of the international workshop on operator theory and its applications, IWOTA-98, Groningen, Netherlands, June 30-July 3, 1998. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 124, 217-241 (2001).
The author gives a summary of the recent results concerning on the asymptotic behavior of Toeplitz determinants with Fisher-Hartwig singularities and describes the main ideas of the proofs which were given in his dissertation [“Toeplitz determinants with several Fisher-Hartwig singularities”, Chemnitz (1997; Zbl 0910.47020)]. This method allows to consider all known cases of the Fisher-Hartwig conjecture.
For the entire collection see [Zbl 0966.00029].

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