We study the cyclic vectors and spanning set of circle for $\ell^p\_\beta(\mathbb{Z})$ spaces all sequences $u= (u\_n ){n\in \mathbb{Z}}$ such that $(u\_n (1+|n|)^{\beta} \mathbb{Z}} \in \ell^p(\mathbb{Z})$ , with $p>1$ $\beta>0$. The uniqueness distribution on whose Fourier coefficients are in $\ell^q\_{-\beta}(\mathbb{Z})$ is spaces, where $q$ conjugate $p$. Our characterizations given terms ...

Let F be a family of convex figures in the plane. We say that F has property T if there exist a line intersecting every member of F . Also, we say that the family F has property T (k) if every k−membered subfamily of F has property T . In this talk we will give some results concerning families of translates of the unit disc which have property T (3) or T (4).

For functions fit) satisfying certain growth conditions, we consider a sequence of the form {/(c„ — /)}, nonfundamental in L^R), and find a representation for those functions which are in the closure of its linear span. Some theorems concerning degree of approximation are also proved. In [1], we found necessary and sufficient conditions for a sequence of the form {ficn — t)} to be fundamental i...

We show that the visibility graph of a set of non-intersecting translates of the same compact convex object in R always contains a Hamiltonian path. Furthermore, we show that every other edge in the Hamiltonian path can be used to obtain a perfect matching that is realized by a set of non-intersecting lines of sight. ? 2001 Elsevier Science B.V. All rights reserved.