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Global Cm-Approximations in
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J.-P. Jurzak
Published/Copyright:
June 7, 2010
Abstract
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 εα(n) → 0 such that | Dαƒn(x) – Dαƒ(x) | ≤ εα(n)hα(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 Cm(Ω, ℝ) are obtained with Ω open subset of .
Received: 2003-04-01
Revised: 2003-12-05
Published Online: 2010-06-07
Published in Print: 2004-December
© Heldermann Verlag
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