Publications of the Scuola Normale Superiore

Analytic convexity and the principle of Phragmen-Lindeloff

Authors: Andreotti, Aldo, Nacinovich, Mauro

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  • ISBN 978-88-7642-243-0
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  • Due: May 15, 2007
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.

Buy this book

Softcover $24.95 net
( price for USA )
  • ISBN 978-88-7642-243-0
  • free shipping for individuals worldwide
  • Due: May 15, 2007

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Bibliographic Information

Bibliographic Information
Book Title
Analytic convexity and the principle of Phragmen-Lindeloff
Series Title
Publications of the Scuola Normale Superiore
Copyright
1980
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
Softcover ISBN
978-88-7642-243-0
Edition Number
1
Topics