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Keywords
- analytic convexity
About this book
We consider in Rn a differential operator P(D), P a polynomial, with constant coefficients. Let U be an open set in Rn and A(U) be the space of real analytic functions on U. We consider the equation P(D)u=f, for f in A(U) and look for a solution in A(U). Hormander proved a necessary and sufficient condition for the solution to exist in the case U is convex. From this theorem one derives the fact that if a cone W admits a Phragmen-Lindeloff principle then at each of its non-zero real points the real part of W is pure dimensional of dimension n-1. The Phragmen-Lindeloff principle is reduced to the classical one in C. In this paper we consider a general Hilbert complex of differential operators with constant coefficients in Rn and we give, for U convex, the necessary and sufficient conditions for the vanishing of the H1 groups in terms of the generalization of Phragmen-Lindeloff principle.
Bibliographic Information
Book Title: Analytic convexity and the principle of Phragmen-Lindeloff
Authors: Aldo Andreotti, Mauro Nacinovich
Series Title: Publications of the Scuola Normale Superiore
Publisher: Edizioni della Normale Pisa
Copyright Information: Edizioni della Normale 1980
Softcover ISBN: 978-88-7642-243-0Published: 01 October 1980
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Number of Pages: 184