| Analytic Convexity and the Principle of Phragmen-Lindeloff Contributor(s): Andreotti, Aldo (Author), Nacinovich, Mauro (Author) |
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ISBN: 8876422439 ISBN-13: 9788876422430 Publisher: Edizioni Della Normale OUR PRICE: $23.70 Product Type: Paperback Published: October 1980 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Calculus |
| Dewey: 515 |
| Series: Publications of the Scuola Normale Superiore |
| Physical Information: 184 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |