Wiener-Hopf determinants with Fisher-Hartwig symbols

Details Wiener-Hopf determinants with Fisher-Hartwig symbols Wiener-Hopf determinants with Fisher-Hartwig symbols

2002-05-17

arxiv.org/abs/math/0205198v3

Mathematics

Functional Analysis

Scientific paper

With localization techniques one can obtain general limit theorems for Toeplitz determinants with Fisher-Hartwig singularities from the asymptotics for any symbol with one singularity of general type. There exists a family of these for which the determinants can be evaluated explicitly and their asymptotics determined. But for the Wiener-Hopf analogue, although there are likely analogous localization techniques, there is not a single example known of a symbol with Fisher-Hartwig singularity for which the determinant can be evaluated explicitly. In this paper we determine the asymptotics of Wiener-Hopf determinants for a symbol with one Fisher-Hartwig singularity of general type. We do this by showing that it is asymptotically equal to a Toeplitz determinant with symbol having the corresponding singularity.

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