Abstract
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?
Citation
Bernard Beauzamy. "Stability of the solutions of differential equations." Illinois J. Math. 43 (1) 151 - 158, Spring 1999. https://doi.org/10.1215/ijm/1255985342
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