ORCID Profile
0009-0009-5965-3018
Current Organisations
University of Melbourne
,
Pennsylvania State University
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Publisher: Element d.o.o.
Date: 2022
Publisher: American Mathematical Society
Date: 23-02-2023
DOI: 10.1090/PSPUM/105/13
Publisher: American Mathematical Society (AMS)
Date: 21-06-2021
DOI: 10.1090/PROC/15538
Abstract: Let 1 p â 1 \\infty and let n â„ 1 n\\geq 1 . It is proved that a function f : R â C f:\\mathbb {R}\\to \\mathbb {C} is n n -times FrĂ©chet differentiable on S p \\mathcal {S}^p at every self-adjoint operator if and only if f f is n n -times differentiable, f âČ , f , ⊠, f ( n ) fâ,f,\\ldots ,f^{(n)} are bounded and f ( n ) f^{(n)} is uniformly continuous.
Publisher: Elsevier BV
Date: 11-2023
Publisher: European Mathematical Society - EMS - Publishing House GmbH
Date: 12-05-2022
DOI: 10.4171/JNCG/459
Publisher: Elsevier BV
Date: 2023
Publisher: Springer Science and Business Media LLC
Date: 23-02-2019
Publisher: Springer Science and Business Media LLC
Date: 22-03-2019
Publisher: Springer Science and Business Media LLC
Date: 30-10-2019
Publisher: Pleiades Publishing Ltd
Date: 04-2021
Publisher: Springer Science and Business Media LLC
Date: 13-05-2020
Publisher: Public Library of Science (PLoS)
Date: 17-08-1970
Publisher: Springer Science and Business Media LLC
Date: 08-2022
Publisher: Elsevier BV
Date: 11-2020
Publisher: Elsevier BV
Date: 10-2017
Publisher: Elsevier BV
Date: 08-2019
Publisher: Springer Science and Business Media LLC
Date: 30-07-2021
Publisher: AIP Publishing
Date: 04-2022
DOI: 10.1063/5.0056289
Abstract: In this paper, we establish Cwikel-type estimates for noncommutative tori for any dimension n â„ 2. We use them to derive CwikelâLiebâRozenblum inequalities and LiebâThirring inequalities for negative eigenvalues of fractional Schrödinger operators on noncommutative tori. The latter leads to a Sobolev inequality for noncommutative tori. On the way, we establish a âborderline versionâ of the abstract BirmanâSchwinger principle for the number of negative eigenvalues of relatively compact form perturbations of a non-negative semi-bounded operator with isolated 0-eigenvalue.
Publisher: Cambridge University Press (CUP)
Date: 04-12-2017
Abstract: If $c$ is in the main cardioid of the Mandelbrot set, then the Julia set $J$ of the map $\\unicode[STIX]{x1D719}_{c}:z\\mapsto z^{2}+c$ is a Jordan curve of Hausdorff dimension $p\\in [1,2)$ . We provide a full proof of a formula for the Hausdorff measure on $J$ in terms of singular traces announced by the first named author in 1996.
Publisher: Elsevier BV
Date: 09-2022
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Edward McDonald.