Uniform convergence in von Neumann's ergodic theorem in the absence of a spectral gap

Ben-Artzi, Jonathan ORCID: https://orcid.org/0000-0001-6184-9313 and Morisse, Baptiste 2021. Uniform convergence in von Neumann's ergodic theorem in the absence of a spectral gap. Ergodic Theory and Dynamical Systems 41 (6) , pp. 1601-1611. 10.1017/etds.2020.30

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Abstract

Von Neumann’s original proof of the ergodic theorem is revisited. A uniform convergence rate is established under the assumption that one can control the density of the spectrum of the underlying self-adjoint operator when restricted to suitable subspaces. Explicit rates are obtained when the bound is polynomial, with applications to the linear Schrödinger and wave equations. In particular, decay estimates for time averages of solutions are shown.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Cambridge University Press (CUP)
ISSN:	0143-3857
Funders:	EPSRC
Date of First Compliant Deposit:	5 March 2020
Date of Acceptance:	4 March 2020
Last Modified:	08 Nov 2023 03:07
URI:	https://orca.cardiff.ac.uk/id/eprint/130122

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