ABSTRACT
Given a positive real number ft, and a function B from lRd into IR, we call “ cardinal Schoenberg’s approximation using B ” , or simply “Schoenberg’s ap proximation” , the operation which, from a vector y = (2/j)j=i,..,n such that the summation in (1.1) is convergent, gives the function ay (or simply denoted a) defined by
“ ( i - i )
This operation was introduced by I.J. Schoenberg [14] in one dimension (d = 1) when B is a polynomial R-spline (in this case, there is no problem of convergence since B has compact support); this is the reason why this operator is called Schoenberg’s approximation. For details on, or around, Schoenberg’s approximation, see the survey papers [2,3,4,8,10].
