On the Inverse and Determinant of Certain Truncated Wiener-Hopf Operators

Details On the Inverse and Determinant of Certain Truncated Wiener-Hopf Operators On the Inverse and Determinant of Certain Truncated Wiener-Hopf Operators

2006-05-02

arxiv.org/abs/math/0605076v3

Mathematics

Functional Analysis

21 pages. Version 3 has improved proofs and treats the case of two simple zeros as well as one double zero

Scientific paper

The solution of a problem arising in integrable systems requires sharp asymptotics for the inverses and determinants of truncated Wiener-Hopf operators, both in the regular case (where the non-truncated Wiener-Hopf operator is invertible) and in singular cases. This paper treats the singular cases where the symbol of the Wiener-Hopf operator has one double zero or two simple zeros. We find formulas for the inverses that hold uniformly throughout the underlying interval with very small error, and formulas for the determinants with very small error.

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