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Inverse scattering problem for a special class of canonical systems and non-linear Fourier integral. Part I: asymptotics of eigenfunctions

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S. Kupin, F. Peherstorfer, A. Volberg, P. Yuditskii

Mathematical Physics · Submitted 4 Nov 2005

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

The authors' main claim This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schr\"odinger) operator.

how it is stated · asserted 0.98 read the record →

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arXiv IDmath-ph/0511016 (version 1)
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CitationA. Volberg, F. Peherstorfer, P. Yuditskii, S. Kupin. "Inverse scattering problem for a special class of canonical systems and non-linear Fourier integral. Part I: asymptotics of eigenfunctions." arXiv:math-ph/0511016 (2005). https://pith.science/paper/G4JS5DLT
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,632 input tokens.

What the abstract itself states, as probabilities: claims first 0.12 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.92 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schr\"odinger) operator.

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 An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. background 1.00 0.03 0.04 asserted 1.00
s1 The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. gap 0.87 0.06 0.03 asserted 1.00
s2 This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. contribution 0.93 0.61 0.11 asserted 0.97
s3 This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schr\"odinger) operator. result 0.78 0.86 0.82 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 0.97.

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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

An original approach to the inverse scattering for Jacobi matrices was suggested in a recent paper by Volberg-Yuditskii. The authors considered quite sophisticated spectral sets (including Cantor sets of positive Lebesgue measure), however they did not take into account the mass point spectrum. This paper follows similar lines for the continuous setting with an absolutely continuous spectrum on the half-axis and a pure point spectrum on the negative half-axis satisfying the Blaschke condition. This leads us to the solution of the inverse scattering problem for a class of canonical systems that generalizes the case of Sturm-Liouville (Schr\"odinger) operator.

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