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Analytic convexity and the principle of Phragmen-Lindeloff

Publications of the Scuola Normale Superiore

Format: Paperback
Publisher: Birkhauser Verlag AG, Pisa, Italy
Imprint: Scuola Normale Superiore
Published: 1st Oct 1980
Dimensions: w 170mm h 240mm
ISBN-10: 8876422439
ISBN-13: 9788876422430
Barcode No: 9788876422430
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.

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