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Exponential Riesz bases of subspaces and divided differences

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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S.A. Avdonin, S.A.Ivanov

Functional Analysis · Submitted 26 Mar 2001

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

The authors' main claim We have generalized this result for groups with arbitrary number of close points and obtained a full description of Riesz bases of exponential divided differences.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0103160 (version 1)
Pith IDKFUPAJLP, Pith's permanent record of this paper and its review
CitationS.A. Avdonin, S.A.Ivanov. "Exponential Riesz bases of subspaces and divided differences." arXiv:math/0103160 (2001). https://pith.science/paper/KFUPAJLP
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,569 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case when the groups consist of equal number of points all of them are close enough to integers. We have generalized this result for groups with arbitrary number of close points and obtained a full description of Riesz bases of exponential divided differences. The application to a control problem is presented.

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 Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. background 0.93 0.32 0.04 asserted 0.57
s1 Ullrich has proved the basis property of the divided differences of exponentials in the case when the groups consist of equal number of points all of them are close enough to integers. background 1.00 0.03 0.07 asserted 1.00
s2 We have generalized this result for groups with arbitrary number of close points and obtained a full description of Riesz bases of exponential divided differences. contribution 0.81 0.96 0.85 asserted 1.00
s3 The application to a control problem is presented. contribution 0.88 0.74 0.05 asserted 0.96

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

What was examined, and what was not

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  • S sections
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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

Linear combinations of exponentials $e^{i\lambda_kt}$ in the case where the distance between some points $\lambda_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case when the groups consist of equal number of points all of them are close enough to integers. We have generalized this result for groups with arbitrary number of close points and obtained a full description of Riesz bases of exponential divided differences. The application to a control problem is presented.

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