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Chebyshevian splines

Zygmunt Wronicz — 1990

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....

On approximation by Chebyshevian box splines

Zygmunt Wronicz — 2002

Annales Polonici Mathematici

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 w j are of the form w j ( x ) = W j ( v n + j · x ) , where the functions W j are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.

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