Projective descriptions of spaces of functions and distributions

Abstract

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by seminorms, which are defined by a combination of classical norms and multiplication or convolution with certain functions. These seminorms are simpler than the ones given by a supremum over bounded or compact sets. K E Y W O R D Sbounded sets, compact sets, distribution spaces, 𝑝-integrable smooth functions, topology of uniform convergence on bounded sets, topology of uniform convergence on compact setsThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.