Open Access
Spring 1999 Stability of the solutions of differential equations
Bernard Beauzamy
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Illinois J. Math. 43(1): 151-158 (Spring 1999). DOI: 10.1215/ijm/1255985342


We introduce a new norm (derived from Bombieri's norm for polynomials) on a class of functions on the complex plane. This norm is hilbertian, and can be viewed as a weighted $L_{2}$ norm (or a weighted $l_{2}$ norm). It allows us to give quantitative results of the following sort: If we solve $P(D)u = f$ (with boundary conditions), and if we modify $f$, how is the solution $u$ modified?


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Bernard Beauzamy. "Stability of the solutions of differential equations." Illinois J. Math. 43 (1) 151 - 158, Spring 1999.


Published: Spring 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0937.30004
MathSciNet: MR1665661
Digital Object Identifier: 10.1215/ijm/1255985342

Primary: 35A25
Secondary: 30C10 , 35C99 , 46N20

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 1 • Spring 1999
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