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Property C for ODE and applications to inverse problems

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A.G.Ramm

Mathematical Physics · Submitted 25 Nov 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis.

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arXiv IDmath-ph/9911032 (version 1)
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CitationA.G.Ramm. "Property C for ODE and applications to inverse problems." arXiv:math-ph/9911032 (1999). https://pith.science/paper/RFT4OWEC
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,589 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.77 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Property C stands for completeness of the set of products of solutions to homogeneous linear differential equations. property C is proved in various formulations for Schr\"odinger operators. Many applications of this property to inverse problems and inverse scattering problems are given. It is shown what part of the fixed-energy phase shifts determines a compactly supported potential uniquely. It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Property C stands for completeness of the set of products of solutions to homogeneous linear differential equations. property C is proved in various formulations for Schr\"odinger operators. background 0.95 0.20 0.14 asserted 1.00
s1 Many applications of this property to inverse problems and inverse scattering problems are given. background 0.61 0.33 0.08 asserted 0.99
s2 It is shown what part of the fixed-energy phase shifts determines a compactly supported potential uniquely. result 0.96 0.78 0.17 asserted 1.00
s3 It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis. result 0.93 0.83 0.42 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Property C stands for completeness of the set of products of solutions to homogeneous linear differential equations. property C is proved in various formulations for Schr\"odinger operators. Many applications of this property to inverse problems and inverse scattering problems are given. It is shown what part of the fixed-energy phase shifts determines a compactly supported potential uniquely. It is shown that the Newton-Sabatier method is not really an inversion method but a parameter-fitting procedure and it is proved that this procedure cannot recover a generic potential, in particular, any potential which is not analytic in a neighborhood of the positive real axis.

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