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Zeitschrift für Analysis und ihre Anwendungen


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Volume 1, Issue 2, 1982, pp. 1–5
DOI: 10.4171/ZAA/9

Published online: 1982-04-30

Über das Reduktionsverfahren für diskrete Wiener-Hopf-Gleichungen mit unstetigem Symbol

Albrecht Böttcher[1] and Bernd Silbermann[2]

(1) Technische Universität Chemnitz, Germany
(2) Technische Universität Chemnitz, Germany

The results of the paper complete and improve some hitherto existing results about the reduction method for discrete Wiener-Hopf equations with discontinuous symbol and, on the other hand, illustrate some new aspects of this set of problems. Thus, it is proved that if the reduction method in $l^p(1 \leq p < \infty)$ is applicable to the Toeplitz operators $T(a_r), a_r \in L^{\infty} (r = 1, \dots, R)$ and if $a_1, \dots, a_R$ have no common singularities (discontinuities), then it is applicable to $T(a_1 \dots a_R)$. Furthermore, there is proved that for a large class of piecewise continuous symbols the reduction method in $L^p$ is applicable to $T(a)$ if and only if both $T(a)$ and $T(\bar {a})$ are invertible.

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Böttcher Albrecht, Silbermann Bernd: Über das Reduktionsverfahren für diskrete Wiener-Hopf-Gleichungen mit unstetigem Symbol. Z. Anal. Anwend. 1 (1982), 1-5. doi: 10.4171/ZAA/9