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Zeitschrift für Analysis und ihre Anwendungen

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Volume 8, Issue 4, 1989, pp. 293–306
DOI: 10.4171/ZAA/355

Published online: 1989-08-31

A. Symbol Calculus for the Algebra Generated by Shift Operators

Steffen Roch[1] and Bernd Silbermann[2]

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

We describe the algebraical structure of the algebra generated by the shift operator and by one of its left-inverses and construct a symbol for the invertibility of an operator modulo the quasicommutator ideal. The correspondence between this symbol and the invertibility and Fredholmness of elements of this algebra are studied.

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Roch Steffen, Silbermann Bernd: A. Symbol Calculus for the Algebra Generated by Shift Operators. Z. Anal. Anwend. 8 (1989), 293-306. doi: 10.4171/ZAA/355