Local H\\"older Stability in the Inverse Steklov and Calder\\'on Problems\n for Radial Schr\\"odinger operators and Quantified Resonances
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Bibliographic record
Abstract
We obtain H\\"older stability estimates for the inverse Steklov and Calder\\'on\nproblems for Schr\\"odinger operators corresponding to a special class of $L^2$\nradial potentials on the unit ball. These results provide an improvement on\nearlier logarithmic stability estimates obtained in \\cite{DKN5} in the case of\nthe the Schr\\"odinger operators related to deformations of the closed Euclidean\nunit ball. The main tools involve: i) A formula relating the difference of the\nSteklov spectra of the Schr\\"odinger operators associated to the original and\nperturbed potential to the Laplace transform of the difference of the\ncorresponding amplitude functions introduced by Simon \\cite{Si1} in his\nrepresentation formula for the Weyl-Titchmarsh function, and ii) A key moment\nstability estimate due to Still \\cite{St}. It is noteworthy that with respect\nto the original Schr\\"odinger operator, the type of perturbation being\nconsidered for the amplitude function amounts to the introduction of a finite\nnumber of negative eigenvalues and of a countable set of negative resonances\nwhich are quantified explicitly in terms of the eigenvalues of the\nLaplace-Beltrami operator on the boundary sphere.\n
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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