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CONTENTSIntroduction...........................................................................................................5I. Canonical complete Chebyshev systems 1. Canonical complete Chebyshev systems.......................................................7 2. Interpolation by generalized polynomials and divided differences................12 3. The Markov inequality for generalized polynomials......................................16II. Chebyshevian splines 1. Basic properties...........................................................................................18 2....
We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
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.
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