On the growth of Fourier multipliers

被引：0

作者：

Battseren, Bat-Od ^{[1
,2
]}

机构：

[1] Univ Cote Azur, Lab Jean Alexandre Dieudonne LJAD, F-06108 Nice, France

[2] Vanderbilt Univ, Dept Math, 1326 Stevenson Ctr, Nashville, TN 37240 USA

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2024年 / 18卷 / 04期

关键词：

locally compact groups; group algebras; Fourier multipliers; weak amenability; rapid decay property; L-P-SPACES; BOUNDED MULTIPLIERS; SCHUR MULTIPLIERS; ALGEBRA; LATTICES; METRICS;

D O I：

10.4171/JNCG/551

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a sequence of functions, namely, tame cuts, in the Fourier algebra A(G) of a locally compact group G, which satisfies certain convergence and growth conditions. This new consideration allows us to give a group admitting a Fourier multiplier that is not completely bounded. Furthermore, we show that the induction map MA(F) ! MA(G) is not always continuous. We also show how Liao's property (TSchur, G, K) opposes tame cuts. Some examples are provided.

引用

页码：1209 / 1228

页数：20

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