Basis in the space of C ∞-functions on a graduated sharp cusp

Abstract

Using the basis in the space of Whitney functions ε(K), where K ℝ is the closure of a union of a sequence of closed intervals tending to a point, we construct a special basis in the space C ∞[0,1] and then a basis in the space of C ∞-functions on a graduated sharp cusp with arbitrary sharpness. © 2003 Mathematica Josephina, Inc.