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On Szegő Formulas for Truncated Wiener–Hopf Operators

  • Alexander V. SobolevEmail author
Open Access
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Abstract

We consider functions of multi-dimensional versions of truncated Wiener–Hopf operators with smooth symbols, and study the scaling asymptotics of their traces. The obtained results extend the asymptotic formulas obtained by H. Widom in the 1980’s to non-smooth functions, and non-smooth truncation domains. The obtained asymptotic formulas are used to analyse the scaling limit of the spatially bipartite entanglement entropy of thermal equilibrium states of non-interacting fermions at positive temperature.

Keywords

Non-smooth functions of Wiener–Hopf operators Asymptotic trace formulas Entanglement entropy 

Mathematics Subject Classification

Primary 47G30 35S05 Secondary 45M05 47B10 47B35 

Notes

Acknowledgements

This paper grew out of numerous discussions with H. Leschke and W. Spitzer, who have author’s deepest gratitude. A part of this paper was written during several visits of the author to the FernUniversität Hagen in 2015-2016.

The author was supported by EPSRC grant EP/J016829/1.

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Copyright information

© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsUniversity College LondonLondonUK

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