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An inverse for the Gohberg-Krupnik symbol map

Published online by Cambridge University Press:  14 November 2011

Martin Costabel
Martin Costabel
Affiliation:
Fachbereich Mathematik der Technischen Hochschule Darmstadt, Germany
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Synopsis

It is shown that the elements of the closed operator algebra generated by one-dimensional singular integral operators with piecewise continuous coefficients with a fixed finite set of points of discontinuity can be written as the sum of a singular integral operator, a compact operator, and generalized Mellin convolutions. Their Gohberg-Krupnik symbol is given in terms of the Mellin transform. This gives an explicit construction of an operator with prescribed Gohberg—Krupnik symbol.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 1-2 , 1980 , pp. 153 - 165
Copyright
Copyright © Royal Society of Edinburgh 1980

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