Pith. Sign in

RECORD

Norms of Modes and Quasi-modes revisited

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
John A. Toth, Steve Zelditch

Analysis of PDEs · Submitted 8 Feb 2002

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

The authors' main claim We give a new proof of the main result of our paper ``Riemannian manifolds with uniformly bounded eigenfunctions' (Duke Math J. 111 (2002), 97-132), based on the analysis of quasi-modes and Birkhoff normal forms.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0202074 (version 1)
Pith IDIVBPUHUH, Pith's permanent record of this paper and its review
CitationJohn A. Toth, Steve Zelditch. "Norms of Modes and Quasi-modes revisited." arXiv:math/0202074 (2002). https://pith.science/paper/IVBPUHUH
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,588 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.56 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

This is a partly expository, partly new paper on sup norm estimates of eigenfunctions. The focus is on the quantum completely integrable case. We give a new proof of the main result of our paper ``Riemannian manifolds with uniformly bounded eigenfunctions' (Duke Math J. 111 (2002), 97-132), based on the analysis of quasi-modes and Birkhoff normal forms. We also discuss related issues of resonant normal forms and tunnelling between tori.

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 This is a partly expository, partly new paper on sup norm estimates of eigenfunctions. contribution 0.71 0.37 0.05 asserted 1.00
s1 The focus is on the quantum completely integrable case. background 0.63 0.17 0.04 asserted 1.00
s2 We give a new proof of the main result of our paper ``Riemannian manifolds with uniformly bounded eigenfunctions' (Duke Math J. 111 (2002), 97-132), based on the analysis of quasi-modes and Birkhoff normal forms. contribution 0.97 0.87 0.41 asserted 1.00
s3 We also discuss related issues of resonant normal forms and tunnelling between tori. contribution 0.99 0.66 0.04 asserted 0.85

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

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

This is a partly expository, partly new paper on sup norm estimates of eigenfunctions. The focus is on the quantum completely integrable case. We give a new proof of the main result of our paper ``Riemannian manifolds with uniformly bounded eigenfunctions' (Duke Math J. 111 (2002), 97-132), based on the analysis of quasi-modes and Birkhoff normal forms. We also discuss related issues of resonant normal forms and tunnelling between tori.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

Papers whose main result relates to this one's

How each label was checked · JSON

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.