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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Localizable analytically uniform spaces and the fundamental principle


Author: Sönke Hansen
Journal: Trans. Amer. Math. Soc. 264 (1981), 235-250
MSC: Primary 35E20; Secondary 46F05
DOI: https://doi.org/10.1090/S0002-9947-1981-0597879-2
MathSciNet review: 597879
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Abstract: The Fundamental Principle of Ehrenpreis states that the solutions of homogeneous linear partial differential equations with constant coefficients have natural integral representations. Using the Oka-Cartan procedure Ehrenpreis derived this theorem for spaces of functions and distributions which he called localizable analytically uniform (LAU-spaces). With a new definition of LAU-spaces we explain how Hörmander's results on cohomology with bounds fit into Ehrenpreis' method of proof of the Fundamental Principle. Furthermore, we show that many of the common Fréchet-Montel spaces of functions are LAU-spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0597879-2
Article copyright: © Copyright 1981 American Mathematical Society