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Beurling density on expansible locally compact groups and systems of translations
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.jmaa.2020.124319
N.S. Seyedi , R.A. Kamyabi Gol

Abstract In this paper, we investigate some properties of the expansive automorphisms on expansible locally compact groups. We define the upper and lower Beurling densities on expansible locally compact groups. Using this definition, we show that if for some 1 p ′ ∞ , the finite union of translates ∪ k = 1 n T p ( f k , Γ k ) is a p ′ -Bessel sequence, then the upper Beurling density is finite, and if ∪ k = 1 n T p ( f k , Γ k ) is a ( C q ) -system, then the upper Beurling density cannot be finite. In particular, we conclude that there exists no p ′ -Bessel ( C q ) -system in L p ( G ) of the form ∪ k = 1 n T p ( f k , Γ k ) , where G is an expansible group.

中文翻译:

可扩展局部紧致群和翻译系统的 Beurling 密度

摘要 在本文中,我们研究了可扩展局部紧群上的可扩展自同构的一些性质。我们定义了可扩展局部紧群上的上下 Beurling 密度。使用这个定义,我们证明如果对于某个 1 p ′ ∞ ,平移 ∪ k = 1 n T p ( fk , Γ k ) 的有限并集是 ap ′ -Bessel 序列,那么上 Beurling 密度是有限的,如果∪ k = 1 n T p ( fk , Γ k ) 是 ( C q ) -系统,则上 Beurling 密度不可能是有限的。特别地,我们得出结论,在 L p ( G ) 中不存在形式为 ∪ k = 1 n T p ( fk , Γ k ) 的 p ′ -Bessel ( C q ) - 系统,其中 G 是一个可扩展群。
更新日期:2020-10-01
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