Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 597879
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35E20, 46F05

Retrieve articles in all journals with MSC: 35E20, 46F05

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society