Analytic convexity and the principle of Phragmen-Lindeloff (Paperback)

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.

General

Imprint:	Scuola Normale Superiore
Country of origin:	Italy
Series:	Publications of the Scuola Normale Superiore
Release date:	October 1980
First published:	1980
Authors:	Aldo Andreotti • Mauro Nacinovich
Dimensions:	240 x 170mm (L x W)
Format:	Paperback
Pages:	184
ISBN-13:	978-88-7642-243-0
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
LSN:	88-7642-243-9
Barcode:	9788876422430

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