کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415033 1334901 2016 42 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Finite products sets and minimally almost periodic groups
ترجمه فارسی عنوان
مجموعه های محصولات محدود و گروه های حداقل تقریبا دوره ای
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We characterize those locally compact, second countable, amenable groups in which a density version of Hindman's theorem holds and those countable, amenable groups in which a two-sided density version of Hindman's theorem holds. In both cases the possible failure can be attributed to an abundance of finite-dimensional unitary representations, which allows us to construct sets with large density that do not contain any shift of a set of measurable recurrence, let alone a shift of a finite products set. The possible success is connected to the ergodic-theoretic phenomenon of weak mixing via a two-sided version of the Furstenberg correspondence principle.We also construct subsets with large density that are not piecewise syndetic in arbitrary non-compact amenable groups. For countably infinite amenable groups, the symbolic systems associated to such sets admit invariant probability measures that are not concentrated on their minimal subsystems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 270, Issue 6, 15 March 2016, Pages 2126-2167
نویسندگان
, , , ,