Temperate distributions with locally finite support and spectrum on Euclidean spaces

Measures with locally finite support and spectrum.

The goal of this paper is the construction of measures μ on R(n)enjoying three conflicting but fortunately compatible properties: (i) μ is a sum of weighted Dirac masses on a locally finite set, (ii) the Fourier transform μ f μ is also a sum of weighted Dirac masses on a locally finite set, and (iii) μ is not a generalized Dirac comb. We give surprisingly simple examples of such measures. These...

Locally Peripherally Euclidean Spaces Are Locally Euclidean, Ii.

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

A Characterization of Locally Euclidean Spaces

Topology on locally finite metric spaces

The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry, Computer Science, Topological Graph Theory and Metric Geometry. In this paper we propose the basic notions of such a theory and some applications: we replace the cl...