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Transactions of the American Mathematical Society

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Limits of functions on groups


Author: Balázs Szegedy
Journal: Trans. Amer. Math. Soc. 370 (2018), 8135-8153
MSC (2010): Primary 05D99; Secondary 43A99
DOI: https://doi.org/10.1090/tran/7432
Published electronically: August 9, 2018
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Abstract: Our goal is to develop a limit approach for a class of problems in additive combinatorics that is analogous to the limit theory of dense graph sequences. We introduce a metric, convergence and limit objects for functions on discrete groups and use it to study limits of measurable functions on compact abelian groups. As an application we find exact minimizers for densities of linear configurations of complexity $ 1$.


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Balázs Szegedy
Affiliation: Alfred Renyi Institute of Mathematics, HU 1053 Budapest, Reáltanoda utca 13-15, 1053 Hungary

DOI: https://doi.org/10.1090/tran/7432
Received by editor(s): February 27, 2015
Received by editor(s) in revised form: March 15, 2017
Published electronically: August 9, 2018
Additional Notes: The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement n$^{∘}$617747. The research was partially supported by the MTA Rényi Institute Lendület Limits of Structures Research Group.
Article copyright: © Copyright 2018 American Mathematical Society

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