We derive new convergence results for the Schoenberg operator and more general quasi-interpolation operators. In particular, we prove that natural conditions on the generator function imply convergence of these operators in the Fourier algebra A(Rd) = FL1(Rd) and in S0(R), a function space developed by the first author and often used in time-frequency analysis. As a simple yet very useful conse...

Let G be an infinite compact group and G its dual. For 1< p < oom P(G) is a module over 21(G) A(G), the Fourier algebra of G. For 1 < p, q < o0, let Ip q = HomA(G)( P(G), ?'(G)). If G is abelian, then Jll is the space of LP(G)-multipliers. For 1 < p < 2 and p the conjugate index of p, A(G) -1,1 p,p p, p 2, 2 (G). Further, the space ll is the dual of a space called d p a subspace of eo(G). Using...

We announce the definition of the dual group, GB(^, of the Fourier-Stieltjes algebra, B(G), of a locally compact group G; and we state four main theorems culminating in the result that GB(G) is a locally compact topological group which is topological^ isomorphic to G. This result establishes an explicit dual relationship between a group and its Fourier-Stieltjes algebra. Moreover, this result e...

In this paper we used the finite Fourier transformation to obtain the polar decomposition of the q-deformed boson algebra with q a root of unity. Since the q-deformed boson algebra was known [1,2], much work has been accomplished in this direction [3-8]. It is well known that this algebra has an infinite dimensional representation when the deformation parameter q is real, while it has a finite ...

It is well known that the Galilei algebra is a sub algebra of Poincare algebra in one space dimension more. 1 This fact allows us to relate relativistic Poincare and Galilean theories. An interesting point is that Galilei transformations in two space dimensions are contained in the usual Poincare transformations? This enables us to present Poincare spin zero wavefunctions as Fourier transforms ...

For any irrational θ and rational number p/q such that q|qθ−p| < 1, a projection e of trace q|qθ−p| is constructed in the the irrational rotation algebra Aθ that is invariant under the Fourier transform. (The latter is the order four automorphism U 7→ V 7→ U, where U, V are the canonical unitaries generating Aθ .) Further, the projection e is approximately central, the cut down algebra eAθe con...