Resultat negatif en theorie d'approximation de compacts fonctionnels par des varietes analytiques et application a un probleme inverse
Amadeo Irigoyen · 2006 · arXiv
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Abstract (excerpt)
In the theory of approximation there are some problems on approximation of compacts in functional spaces by nonlinear families : first we deal with the polynomial case, and then we consider the analytic case. We demonstrate a negative result in which we claim that an analytic familie of functions with $N$ parameters can not approach the compact $Λ_l(I^s)$ closer than of order $(N\log N)^{\frac{l}{s}}$, when $N$ increases. As applied to an inverse problem in Sturm-Liouville theory, this assertion provides an answer to a question about the best possible reconstruction of the negative potential $
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Metadata source: arXiv