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arXiv · 2011.00146

On the growth of Fourier multipliers

Bat-Od Battseren
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Abstract

We define a sequence of functions, namely tame cuts, in the Fourier algebra $A(G)$ of a locally compact group $G$, that 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 $MA(\Gamma)\rightarrow MA(G)$ is not always continuous. We also show how Liao's Property $(T_{Schur}, G, K)$ opposes tame cuts. Some examples are provided.

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Bat-Od Battseren. 2020-10-31. On the growth of Fourier multipliers. https://arxiv.org/abs/2011.00146

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