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

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.

38 pages, 6 figures

References in corpus (2)

• Dyson's constants in the asymptotics of the determinants of Wiener-Hopf-Hankel operators with the sine kernel
• On the asymptotics of certain Wiener-Hopf-plus-Hankel determinants