Resultat negatif en theorie d'approximation de compacts fonctionnels par des varietes analytiques et application a un probleme inverse
| dc.creator | Irigoyen, Amadeo | |
| dc.date | 2006-01-30 | |
| dc.date.accessioned | 2026-07-07T06:59:28Z | |
| dc.date.available | 2026-07-07T06:59:28Z | |
| dc.description | 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 $Q$ with $m+1$ integrable derivatives, from its eigenvalues and characteristic values of the equation $-y''+ω^2Qy=λy$, when $ω$ increases : we show that it is impossible to get an analytic approximating formula with precision better than of order $(ω\logω)^{-(m+1)}$. Moreover there is from Henkin-Novikova formulas which are almost optimal. | |
| dc.description | 54 pages, in French | |
| dc.identifier | https://arxiv.org/abs/math/0601730 | |
| dc.identifier | http://arxiv.org/abs/math/0601730 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107760 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.title | Resultat negatif en theorie d'approximation de compacts fonctionnels par des varietes analytiques et application a un probleme inverse | |
| dc.type | text |