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Special cases of power decay in multilinear oscillatory integrals

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Dong Dong, Dominique Maldague, Dominick Villano

Classical Analysis and ODEs · Submitted 10 Apr 2019

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

The authors' main claim Consideration of special cases leads to an extended class of examples for which $\lambda$-power decay holds.

how it is stated · asserted 0.99 read the record →

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arXiv ID1904.05428 (version 1)
Pith IDNPVBEXU6, Pith's permanent record of this paper and its review
CitationDominick Villano, Dominique Maldague, Dong Dong. "Special cases of power decay in multilinear oscillatory integrals." arXiv:1904.05428 (2019). https://pith.science/paper/NPVBEXU6
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The compiled record

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, 2,262 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.46 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.56 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. Consideration of special cases leads to an extended class of examples for which $\lambda$-power decay holds.

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 We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. method 0.81 0.89 0.09 asserted 1.00
s1 Consideration of special cases leads to an extended class of examples for which $\lambda$-power decay holds. result 0.85 0.75 0.67 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.98.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered by existing theory. Consideration of special cases leads to an extended class of examples for which $\lambda$-power decay holds.

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