A Note on Hörmander's strongly coprime condition

Abstract

The goal of the paper is to verify Hörmander's strongly coprime condition for two Bessel functions (of the first kind), adjusted not to vanish at zero, whose indices have a certain relationship. These Bessel functions, and , must have indices which differ by a positive integer, i.e., , and the index . As a consequence of satisfying Hörmander's condition, these two functions are then known to generate (algebraically) the space of Fourier transforms of the space , by means of writing The results are also applied to radial functions in R n .