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The finite section method for Toeplitz operators on the quarter-plane with piecewise continuous symbols. (English) Zbl 0549.47010

This paper provides a ”finite section method” for the study of Fredholm properties of multidimensional Toeplitz operators \(T(\phi)=(a_{i-j})\) with piecewise continuous symbol \(\phi\). The technique is based on a tensor-algebraic version of earlier work by the latter author [Math. Nachr. 104, 137-146 (1981; Zbl 0494.47018)] and it considers convergence properties of (tensor products of) sequences of the form \(\sum^{r}_{j=1}\prod^{s}_{k=1}T_ n(\phi^ k_ j)\) as \(n\to\infty \), where the functions \(\phi^ k_ j\) are piecewise continuous and \(T_ n(\phi)\) is the upper-left \(n\times n\) section of \(T(\phi)\). The authors also provide Fredholm and invertibility criteria for compact perturbations of Toeplitz operators.
Reviewer: J.Butz

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators

Citations:

Zbl 0494.47018
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References:

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