2006/02/16 by Eliahu Levy, Levy, Eliahu
Computer Science · Mathematics · #Digital Filter Design and Implementation #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #math.FA #math.GN
paper · pdf · doi:10.48550/arxiv.math/0602360
7 pages, tentative version
arxiv created 2006/02/16 · arxiv updated 2009/12/01
Function (linear) spaces on which an arbitrary function operates (i.e. the space is stable w.r.t. the pointwise unary operation defined by the function) were investigated, for continuous real or complex operations, by deLeeuw-Katznelson, Sternfeld and Weit. They showed that, with suitable assumptions, a real or complex function space on which a non-affine continuous function operates is like an algebra. In this note, however, the point of view is somewhat different: the scalars are any field K, and from the outset no topology or continuity are assumed. Rather, a function space operated by a non-additively-affine (multivariate) function induces a topology on the set on which it is defined and the family of functions which operate on it induces topologies on Kn. These are used to derive a density property and to investigate "homomorphisms" of such spaces w.r.t. the "operations".