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Real roots of polynomials and right inverses for partial differential operators in the space of tempered distributions

Published online by Cambridge University Press:  14 November 2011

Michael Langenbruch
Michael Langenbruch
Affiliation:
Mathematisches Institut der Universität, Einsteinstrasse 62, D-4400 Munster, Germany
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Synopsis

Let P(D) be a partial differential operator with constant coefficients. If P(D) has a continuous linear right inverse in the space of tempered distributions, then P is the product of a polynomial without real roots and a real polynomial admitting a right inverse. If the polynomial P is real and irreducible, then P(D) admits a right inverse in the tempered distributions if and only if P(×) has the property of zeros of R. Thorn.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 169 - 179
Copyright
Copyright © Royal Society of Edinburgh 1990

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