On the growth of Fourier multipliers. (English) Zbl 07926808
Summary: 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 \(MA (\Gamma)\rightarrow MA(G)\) is not always continuous. We also show how Liao’s property \((T_{\mathrm{Schur}},G,K)\) opposes tame cuts. Some examples are provided.
MSC:
| 43A22 | Homomorphisms and multipliers of function spaces on groups, semigroups, etc. |
| 22D15 | Group algebras of locally compact groups |
Keywords:
locally compact groups; group algebras; Fourier multipliers; weak amenability; rapid decay propertyReferences:
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