Positivity in Twisted Convolution Algebra and Fourier Modulation Spaces

Convolution and Homogeneous Spaces

Abstract structure of partial function $*$-algebras over semi-direct product of locally compact groups

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Full Characterization of Embedding Relations between Α-modulation Spaces

In this paper, we consider the embedding relations between any two α-modulation spaces. Based on an observation that the α-modulation space with smaller α can be regarded as a corresponding α-modulation space with larger α, we give a complete characterization of the Fourier multipliers between α-modulation spaces with different α. Then we establish a full version of optimal embedding relations ...

Bilinear Fourier integral operator and its boundedness

We consider the bilinear Fourier integral operatorS(f, g)(x) =ZRdZRdei1(x,)ei2(x,)(x, , ) ˆ f()ˆg()d d,on modulation spaces. Our aim is to indicate this operator is well defined onS(Rd) and shall show the relationship between the bilinear operator and BFIO onmodulation spaces.

A Characterization of Fourier Transforms

The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups Z/nZ, the integers Z, the Torus T and the real line. We also ask a related question for the twisted convolution. In memory of A. Hulanicki.