H\"{o}lder Stability in the Inverse Steklov Problem for Radial Schr\"{o}dinger operators and Quantified Resonances - Laboratoire de Mathématiques de Besançon (UMR 6623) Accéder directement au contenu
Rapport Année : 2022

H\"{o}lder Stability in the Inverse Steklov Problem for Radial Schr\"{o}dinger operators and Quantified Resonances

Résumé

In this paper, we obtain H\"{o}lder stability estimates for the inverse Steklov problem for Schr\"{o}dinger operators corresponding to a special class of $L^2$ radial potentials on the unit ball. These results provide an improvement on earlier logarithmic stability estimates obtained in [8] in the case of the Schr\"{o}dinger operators related to deformations of the closed unit ball. The main tools involve a formula relating the difference of the Steklov spectra of the Schr\"{o}dinger operators associated to the original and perturbed potential to the Laplace transform of the difference of the corresponding amplitude functions introduced by B. Simon and a key moment stability estimate due to Still. It is noteworthy that with respect to the original Schr\"{o}dinger operator, the type of perturbation being considered for the amplitude function amounts to the introduction of a finite number of negative eigenvalues and of a countable set of negative resonances which are quantified explicitly in terms of the eigenvalues of the Laplace-Beltrami operator on the boundary sphere.
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Dates et versions

hal-03883525 , version 1 (05-12-2022)

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Citer

Thierry Daudé, Niky Kamran, François Nicoleau. H\"{o}lder Stability in the Inverse Steklov Problem for Radial Schr\"{o}dinger operators and Quantified Resonances. Université de Franche-Comté (Besançon); McGill University / Université McGill; Nantes Université. 2022. ⟨hal-03883525⟩
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