We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a Hörmander-Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood-Paley type inequalities in group von Neumann algebras, prove Lp estimates for noncommutative Riesz transforms and characterize L∞ → BMO boundedness for radial Fouri...

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

The quaternion Fourier transform (QFT), which is a nontrivial generalization of the real and complex Fourier transform (FT) using quaternion algebra has been of interest to researchers for some years (see e.g. [3, 5]). It was found that many FT properties still hold but others have to be modified. Based on the (right-sided) QFT, one can extend the classical wavelet transform (WT) to quaternion ...

We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).