Physics – Mathematical Physics
Scientific paper
2006-05-17
Physics
Mathematical Physics
40 pages
Scientific paper
We give here some negative results in Sturm-Liouville inverse theory, meaning that we cannot approach any of the potentials with $m+1$ integrable derivatives on $\mathbb{R}^+$ by an $\omega$-parametric analytic family better than order of $(\omega\ln\omega)^{-(m+1)}$. Next, we prove an estimation of the eigenvalues and characteristic values of a Sturm-Liouville operator and some properties of the solution of a certain integral equation. This allows us to deduce from [Henkin-Novikova] some positive results about the best reconstruction formula by giving an almost optimal formula of order of $\omega^{-m}$.
No associations
LandOfFree
Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-490005