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.
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页码：1209 / 1228
页数：20
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