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We study Fourier multipliers on free group $mathbb{F}_infty$ associated with the first segment of the reduced words, and prove that they are completely bounded on the noncommutative $L^p$ spaces $L^p(hat{mathbb{F}}_infty)$ iff their restriction on $L^p(hat{mathbb{F}}_1)=L^p(mathbb{T})$ are completely bounded. As a consequence, every classical Mikhlin multiplier extends to a $L^p$ Fourier multiplier on free groups for all $1<p<infty$.
We study the dual relationship between quantum group convolution maps $L^1(mathbb{G})rightarrow L^{infty}(mathbb{G})$ and completely bounded multipliers of $widehat{mathbb{G}}$. For a large class of locally compact quantum groups $mathbb{G}$ we compl
In this paper, we apply the theory of algebraic cohomology to study the amenability of Thompsons group $mathcal{F}$. We introduce the notion of unique factorization semigroup which contains Thompsons semigroup $mathcal{S}$ and the free semigroup $mat
The noncommutative Fourier transform of the irrational rotation C*-algebra is shown to have a K-inductive structure (at least for a large concrete class of irrational parameters, containing dense $G_delta$s). This is a structure for automorphisms tha
We present several operat
The Fourier(-Stieltjes) algebras on locally compact groups are important commutative Banach algebras in abstract harmonic analysis. In this paper we introduce a generalization of the above two algebras via twisting with respect to 2-cocycles on the g