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).

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).

We describe a non-commutative generalization of the complex Fourier-Mellin transform to Clifford algebra valued signal functions over the domain Rp,q taking values in Cl(p,q), p+q = 2.

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).

For the Lie algebra sl over a p adic eld the Fourier transform of a regular orbital integral is expressed as an integral over all regular orbital integrals with explicit coe cients This expression unlike the Shalika germ expansion is not restricted to orbits of small elements The result gives quite an elementary access to a simple example of Waldspurger s recent theorem on endoscopic transfer o...

Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebra Ŝ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or co...

Abstract. In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study the Fourier and Fourier-Plancherel transforms and prove the Plancherel theorem for compact groupoids. We also study the central functions in the algebra of squa...

Different versions of Wiener’s Tauberian theorem are discussed for the generalized group algebra LI(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener’s Tauberian property is introduced and it is proved that LI(G,A) is weakly Tauberian if and only if A is....

The following is a (very) brief review of linear system theory and Fourier analysis. I work primarily with discrete signals, but each result developed in this review has a parallel in terms of continuous signals and systems. I assume the reader is familiar with linear algebra (as reviewed in my handout Geometric Review of Linear Algebra), and least squares estimation (as reviewed in my handout ...

We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological ∗-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. 1. Definitions and Notations Let S be a locally compact topological semigroup and M(S) be the Banach algebra of all bounded regular Borel measures μ on ...