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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A general formula for fundamental solutions of linear partial differential equations with constant coefficients


Author: Gerhard May
Journal: Proc. Amer. Math. Soc. 122 (1994), 455-461
MSC: Primary 35E05
MathSciNet review: 1211585
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Abstract: In this note we present a formula which furnishes particular fundamental solutions of linear partial differential equations with constant coefficients. Our construction extends an explicit formula of König (to appear) after the procedure of Malgrange (1955-1956). The crucial point is that he works with equations rather than with estimations as in the classical proof of the Malgrange-Ehrenpreis theorem. Following his ideas, we obtain fundamental solutions which are regular in the sense of Hörmander (1983); they are of basic importance. Our formula is as explicit as the zeros of a polynomial in one variable are explicit as functions of the coefficients.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1211585-7
PII: S 0002-9939(1994)1211585-7
Article copyright: © Copyright 1994 American Mathematical Society