June 7, 2010
The convolution of a function with a Diracsequence gives an approximation of by a sequence of functions converging uniformly on compact subsets of as well as its derivatives. The paper studies global estimations on , i.e. there exists functions and a sequence ε α ( n ) → 0 such that | D α ƒ n ( x ) – D α ƒ( x ) | ≤ ε α ( n ) h α ( x ) for all , all | α | ≤ m all n ≥ 1. Special subalgebras of are introduced for the study of the dominated behavior of the convolution process. Some extensions for C m (Ω, ℝ) are obtained with Ω open subset of .