ANALYTIC CONVEXITY AND THE PRINCIPLE OF PHRAGMEN-LINDELOFF by Aldo Andreotti, Mauro Nacinovich ( 9788876422430 )

Item Details

Title:

ANALYTIC CONVEXITY AND THE PRINCIPLE OF PHRAGMEN-LINDELOFF

By:

Format:

Paperback

List price:	£14.99
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ISBN 10:

8876422439

ISBN 13:

9788876422430

Publisher:

BIRKHAUSER VERLAG AG

Pub. date:

1 October, 1980

Series:

Publications of the Scuola Normale Superiore / Crm Series

Pages:

184

Description:

Includes a paper that considers a general Hilbert complex of differential operators with constant coefficients in Rn and offers, for U convex, the necessary and sufficient conditions for the vanishing of the H1 groups in terms of the generalization of Phragmen-Lindeloff principle.

Synopsis:

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.

Illustrations:

bibliography

Publication:

Italy

Imprint:

Scuola Normale Superiore

Returns:

Returnable

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ANALYTIC AND ALGEBRAIC DEPENDENCE OF MEROMORPHIC FUNCTIONS (PB)