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Fredholm and invertibility theory for a special class of Toeplitz + Hankel operators

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arxiv 1110.0577 v1 pith:4GCTFMM3 submitted 2011-10-04 math.FA

Estelle L. Basor , Torsten Ehrhardt This is my paper · ORCID
classification math.FA
keywords fredholmhankelinvertibilityoperatorstheorytoeplitzappliedcase
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abstract

We develop a complete Fredholm and invertibility theory for Toeplitz+Hankel operators $T(a)+H(b)$ on the Hardy space $H^p$, $1<p<\infty$, with piecewise continuous functions $a,b$ defined on the unit circle which are subject to the condition $a(t)a(t^{-1})=b(t)b(t^{-1})$, $|t|=1$. In particular, in the case of Fredholmness, formulas for the defect numbers are established. The results are applied to several important examples.

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  1. A Riemann-Hilbert Approach to Asymptotic Analysis of Toeplitz+Hankel Determinants

    math-ph 2019-09 accept novelty 8.0 of 10

    A 4x4 Riemann-Hilbert formalism gives large-n asymptotics for Toeplitz+Hankel determinants with independent symbols, conditional on a non-degeneracy bound and verified for an explicit family.

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