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Christoffel-Darboux kernels in several real variables

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Dariusz Cichoń, Franciszek H. Szafraniec

Classical Analysis and ODEs · Submitted 16 Sep 2022

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

The authors' main claim The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose.

how it is stated · asserted 0.95 read the record →

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arXiv ID2209.07839 (version 1)
Pith IDSTKZEYE7, Pith's permanent record of this paper and its review
CitationDariusz Cicho\'n, Franciszek H. Szafraniec. "Christoffel-Darboux kernels in several real variables." arXiv:2209.07839 (2022). https://pith.science/paper/STKZEYE7
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,271 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose. Examples of orthogonal polynomials on the unit circle and on the Bernoulli lemniscate are discussed.

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 The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose. contribution 0.90 0.73 0.14 asserted 0.95
s1 Examples of orthogonal polynomials on the unit circle and on the Bernoulli lemniscate are discussed. contribution 0.91 0.71 0.06 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 0.89 · evidence from proof or derivation 0.98.

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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

The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose. Examples of orthogonal polynomials on the unit circle and on the Bernoulli lemniscate are discussed.

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