Density of translates in weighted Lp spaces on locally compact groups

被引:8
作者
Abakumov, Evgeny [1 ]
Kuznetsova, Yulia [2 ]
机构
[1] Univ Paris Est, 5 Blvd Descartes, F-77454 Champs Sur Marne, Marne La Vallee, France
[2] Univ Bourgogne Franche Comte, 16 Route Gray, F-25030 Besancon, France
来源
MONATSHEFTE FUR MATHEMATIK | 2017年 / 183卷 / 03期
关键词
Locally compact groups; Weighted spaces; Hypercyclicity; Translation semigroups; OPERATORS;
D O I
10.1007/s00605-017-1046-x
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a locally compact group, and let 1 <= p < infinity. Consider the weighted L-p-space L-p(G, omega) = {f : integral |f omega|(p) < infinity}, where : omega: G -> R is a positive measurable function. Under appropriate conditions on omega, G acts on L-p (G, omega) by translations. When is this action hypercyclic, that is, there is a function in this space such that the set of all its translations is dense in L-p (G, omega)? Salas (Trans Am Math Soc 347: 993-1004, 1995) gave a criterion of hypercyclicity in the case G = Z. Under mild assumptions, we present a corresponding characterization for a general locally compact group G. Our results are obtained in a more general setting when the translations only by a subset S subset of G are considered.
引用
收藏
页码:397 / 413
页数:17
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