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Chebyshevian box splines were introduced in [5]. The purpose of this paper is to show some new properties of them in the case when the weight functions are of the form
,
where the functions are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.
We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
For , precise conditions on the parameters are given under which the particular superposition operator is a bounded map in the Besov space . The proofs rely on linear spline approximation theory.
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