Truncated Wiener-Hopf operators with Fisher Hartwig singularities
Abstract
We derive the asymptotic behavior of determinants of truncated Wiener-Hopf operators generated by symbols having Fisher-Hartwig singularities. This task is achieved thanks to an asymptotic resolution of the Riemann-Hilbert problem associated to some generalized sine kernel. As a byproduct, we give yet another derivation of the asymptotic behavior of Toeplitz determinants having Fisher-Hartwig singularities. The Riemann-Hilbert problem approach to these asymptotics yields a systematic although quickly cumbersome way to compute their sub-leading asymptotics.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2008
- DOI:
- 10.48550/arXiv.0805.3902
- arXiv:
- arXiv:0805.3902
- Bibcode:
- 2008arXiv0805.3902K
- Keywords:
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- Mathematics - Functional Analysis
- E-Print:
- 68 pages (V3, minor corrections)