Melbourne, Ian and Terhesiu, Dalia (2013) First and higher order uniform dual ergodic theorems for dynamical systems with infinite measure. Israel Journal of Mathematics, Volume 194 (Number 2). pp. 793-830. doi:10.1007/s11856-012-0154-5 ISSN 0021-2172.

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Abstract

We generalize the proof of Karamata’s Theorem by the method of approximation by polynomials to the operator case. As a consequence, we offer a simple proof of uniform dual ergodicity for a very large class of dynamical systems with infinite measure, and we obtain bounds on the convergence rate.
In many cases of interest, including the Pomeau-Manneville family of intermittency maps, the estimates obtained through real Tauberian remainder theory are very weak. Building on the techniques of complex Tauberian remainder theory, we develop a method that provides second (and higher) order asymptotics. In the process, we derive a higher order Tauberian theorem for scalar power series which, to our knowledge, has not previously been covered.

Item Type:	Journal Article
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Israel Journal of Mathematics
Publisher:	Magnes Press
ISSN:	0021-2172
Official Date:	2013
Dates:	Date Event 2013 Published
Volume:	Volume 194
Number:	Number 2
Page Range:	pp. 793-830
DOI:	10.1007/s11856-012-0154-5
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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