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L'Autore dà due criteri necessari e sufficienti perché una funzione possa essere rappresentata da una trasformazione di convoluzione nel caso che il nucleo sia della classe 1 o della classe 3 ed esista un tale che essendo una funzione localmente a variazione limitata.
* Part of this work was done while the second author was on a visit at Tel Aviv University in March 2001
Let f ∈ C[−1, 1] change its convexity finitely many times, in the
interval. We are interested in estimating the degree of approximation of f by
polynomials, and by piecewise polynomials, which are nearly coconvex with
it, namely, polynomials and piecewise polynomials that preserve the convexity
of f except perhaps in some small neighborhoods of the points where f
changes its convexity....
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