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Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems

Amadeo Irigoyen
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Abstract

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 $ω$-parametric analytic family better than order of $(ω\lnω)^{-(m+1)}$. 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 $ω^{-m}$.

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Amadeo Irigoyen. 2006-05-17. Application of approximation theory by nonlinear manifolds in Sturm-Liouville inverse problems. https://doi.org/10.1088/0266-5611%2F23%2F2%2F006

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