Translation invariant subspaces of finite dimension

Abstract

Abstract : Several simple proofs are given of the following theorem. Every finite dimensional translation invariant subspace W of the continuous functions on (minus infinity, infinity), or of the Schwartz distributions on (minus infinity, plus infinity), is spanned by a set of exponential monomials t to the (mu-1) power times e to the (lambda t) power, lambda lambda sub 1, ..., lambda sub k. Thus, W is the solution space o a homogeneous linear ordinary differential equation with constant coefficients. (Author)