Functional calculus estimates for Tadmor-Ritt operators

Felix Schwenninger

RECORD

Functional calculus estimates for Tadmor-Ritt operators

Felix Schwenninger

Functional Analysis · Submitted 30 Jun 2015

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

The authors' main claim We show $H^{\infty}$-functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,883 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.94 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We show $H^{\infty}$-functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor-Ritt operators in terms of the constant dependence. Furthermore, it is shown how discrete square function estimates influence the estimates.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show $H^{\infty}$-functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse.	contribution 0.76	0.95	0.90	asserted 1.00
s1	These estimates are in conformity with the best known power-bounds for Tadmor-Ritt operators in terms of the constant dependence.	interpretation 0.56	0.68	0.13	asserted 0.89
s2	Furthermore, it is shown how discrete square function estimates influence the estimates.	contribution 0.51	0.84	0.07	asserted 1.00

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

We show $H^{\infty}$-functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor-Ritt operators in terms of the constant dependence. Furthermore, it is shown how discrete square function estimates influence the estimates.

Human review

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

How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 2 sentences without a confident label

Cites as background 3 papers

This leads to the study of the $H^∞$-calculus for Tadmor–Ritt operators [ref] .

On functional calculus properties of Ritt operators · Tadmor–Ritt and Kreiss operators · 0.81
This leads to the study of the $H^∞$-calculus for Tadmor–Ritt operators [ref] .

Isometric dilations and $H^\infty$ calculus for bounded analytic semigroups and Ritt operators · Tadmor–Ritt and Kreiss operators · 0.81
In [ref] a suitable $L^p$-version of square function estimates was introduced which then got further adapted to general Banach spaces by Kalton and Weis in the unpublished note [ref] , see also [ref] and the references therein.

The $H^{\infty}$-Functional Calculus and Square Function Estimates · The effect of discrete square function estimates - Hilbert space · 0.87

Discussion

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