Analytic Convexity and the Principle of Phragmen-Lindeloff (Publications of the Scuola Normale Superiore / Crm Series)

Analytic Convexity and the Principle of Phragmen-Lindeloff (Publications of the Scuola Normale Superiore / Crm Series)

By: Mauro Nacinovich (author), Aldo Andreotti (author)Paperback

2 - 4 weeks availability

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.

Create a review

Product Details

  • publication date: 01/10/1980
  • ISBN13: 9788876422430
  • Format: Paperback
  • Number Of Pages: 184
  • ID: 9788876422430
  • ISBN10: 8876422439

Delivery Information

  • Saver Delivery: Yes
  • 1st Class Delivery: Yes
  • Courier Delivery: Yes
  • Store Delivery: Yes

Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly

Close