Related papers: Fourier-Stieltjes transform defined by induced rep…

This work addresses an extension of Fourier-Stieltjes transform of a vector measure defined on compact groups to locally compact groups, by using a group representation induced by a representation of one of its compact subgroups.

Let $G$ be a locally compact group and $1\leq p<\infty$. A continuous unitary representation $\pi\!: G\to B(\mathcal{H})$ of $G$ is an $L^p$-representation if the matrix coefficient functions $s\mapsto \langle \pi(s)x,x\rangle$ lie in…

For a locally compact abelian group $G$, J. L. Taylor (1971) gave a complete characterization of invertible elements in the measure algebra $M(G)$. Using the Fourier-Stieltjes transform, this characterization can be carried out in the…

In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…

The Fourier-Stieltjes and Fourier algebras B(G), A(G) for a general locally compact group G, first studied by P. Eymard, have played an important role in harmonic analysis and in the study of operator algebras generated by G. Recently,…

Let h be a real-analytic function in the neighborhood of some compact set K on the plane. We show that for any complex measure on the Euclidean space of a finite total variation without singular components with the Fourier--Stieltjes…

We prove that if $\rho: A(H) \to B(G)$ is a homomorphism between the Fourier algebra of a locally compact group $H$ and the Fourier-Stieltjes algebra of a locally compact group $G$ induced by a mixed piecewise affine map $\alpha : G \to H$,…

The Fourier and Fourier-Stieltjes algebras over locally compact groupoids have been defined in a way that parallels their construction for groups. In this article, we extend the results on surjectivity or lack of surjectivity of the…

It is a well-known result of Eymard that the Fourier-Stieltjes algebra of a locally compact group $G$ can be identified with the dual of the group $\cs$ $C^{*}(G)$. A corresponding result for a locally compact groupoid $G$ has been…

We extend the theory of Fourier--Stieltjes algebras to the category of twisted actions by \'etale groupoids on arbitrary C*-bundles, generalizing theories constructed previously by B\'{e}dos and Conti for twisted group actions on unital…

The induced representation ${\rm Ind}_H^GS$ of a locally compact group $G$ is the unitary representation of the group $G$ associated with unitary representation $S:H\rightarrow U(V)$ of a subgroup $H$ of the group $G$. Our aim is to develop…

In this paper we prove pointwise and distributional Fourier transform inversion theorems for functions on the real line that are locally of bounded variation, while in a neighbourhood of infinity are Lebesgue integrable or have polynomial…

The notion of Fourier transform is among the more important tools in analysis, which has been generalized in abstract harmonic analysis to the level of abelian locally compact groups. The aim of this paper is to further generalize the…

Inspired by Kalton and Wood's work on group algebras, we describe almost completely contractive algebra homomorphisms from Fourier algebras into Fourier-Stieltjes algebras (endowed with their canonical operator space structure). We also…

Let $G$ be an even orthogonal quasi-split group defined over a local non-archimedean field $F$. We describe the subspace of smooth vectors of the minimal representation of $G(F),$ realized on the space of square-integrable functions on a…

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…

We determine the structure of the weak*-closed $G$-invariant ideals in the Fourier-Stieltjes algebra $B(G)$ of certain groups $G$ by means of a $K$-theoretical obstruction. The groups to which this applies are groups whose only irreducible…

We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two…

Let $G$ be a $p$-adic Lie group with reductive Lie algebra $\mathfrak{g}$. Denote by $D(G)$ the locally analytic distribution algebra of $G$. Orlik-Strauch and Agrawal-Strauch have studied certain exact functors defined on various…

The Fourier coefficients F(t) of a function f on a compact symmetric space U/K are given by integration of f against matrix coefficients of irreducible representations of U. The coefficients depend on a spectral parameter t, which…