Pith. Sign in

RECORD

Rendezvous numbers in normed spaces

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
Balint Farkas, Szilard Gy. Revesz

Classical Analysis and ODEs · Submitted 29 Jul 2005

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

The authors' main claim It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDmath/0507603 (version 2)
Pith IDGHIMHNYB, Pith's permanent record of this paper and its review
CitationBalint Farkas, Szilard Gy. Revesz. "Rendezvous numbers in normed spaces." arXiv:math/0507603 (2005). https://pith.science/paper/GHIMHNYB
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, 5,510 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.44 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In previous papers, we used abstract potential theory, as developed by Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. We introduced energies, Chebyshev constants as two variable set functions, and the modified notion of rendezvous intervals which proved to be rather nicely behaved even for only lower semicontinuous kernels or for not necessarily compact metric spaces. Here we study the rendezvous and average numbers of possibly infinite dimensional normed spaces. It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces. We also observe the connections of these "magical numbers" to Chebyshev constants, Chebyshev radius and entropy. Applying the developed notions with the available methods we calculate the rendezvous numbers or rendezvous intervals of certain concrete Banach spaces. In particular, a satisfactory description of the case of L_p spaces is obtained for all p>0.

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 In previous papers, we used abstract potential theory, as developed by Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. background 1.00 0.67 0.03 asserted 0.99
s1 We introduced energies, Chebyshev constants as two variable set functions, and the modified notion of rendezvous intervals which proved to be rather nicely behaved even for only lower semicontinuous kernels or for not necessarily compact metric spaces. background 0.65 0.83 0.05 asserted 0.99
s2 Here we study the rendezvous and average numbers of possibly infinite dimensional normed spaces. contribution 0.99 0.63 0.06 asserted 0.79
s3 It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces. result 1.00 0.89 0.58 asserted 1.00
s4 We also observe the connections of these "magical numbers" to Chebyshev constants, Chebyshev radius and entropy. result 0.66 0.84 0.07 asserted 0.96
s5 Applying the developed notions with the available methods we calculate the rendezvous numbers or rendezvous intervals of certain concrete Banach spaces. contribution 0.51 0.91 0.08 asserted 0.99
s6 In particular, a satisfactory description of the case of L_p spaces is obtained for all p>0. result 0.96 0.92 0.13 asserted 0.99

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 v2
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

In previous papers, we used abstract potential theory, as developed by Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. We introduced energies, Chebyshev constants as two variable set functions, and the modified notion of rendezvous intervals which proved to be rather nicely behaved even for only lower semicontinuous kernels or for not necessarily compact metric spaces. Here we study the rendezvous and average numbers of possibly infinite dimensional normed spaces. It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces. We also observe the connections of these "magical numbers" to Chebyshev constants, Chebyshev radius and entropy. Applying the developed notions with the available methods we calculate the rendezvous numbers or rendezvous intervals of certain concrete Banach spaces. In particular, a satisfactory description of the case of L_p spaces is obtained for all p>0.

Human review

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

Discussion

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