On some complex spline operators

• Autorzy: Wronicz, Z.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with the space Sn(ΔN) of splines in the complex (or real) variable z of degree n with respect to a given partition ΔN of a rectifiable Jordan curve Γ. We define an operator QN : LP(Γ) → Sn(ΔN), such that QN f = f for f ∈ Sn(ΔN), by means of a system of step functions "biorthogonal" to B-splines and then we estimate the order of approximation of f by QN f in the space Ck(Γ), k ≤ n. We apply the obtained results to approximation of analytic functions in the interior D of a Jordan curve Γ and of class Ck on D (k = 0,..., n - 1) by analytic splines defined in the interior Γ by means of the Cauchy integral. Then we consider the special case, where Γ is the interval [0, 1] and we estimate the order of approximation of f by QN f in the space Wnp([0, 1]) for 1 ≤ p ≤ ∞.

Słowa kluczowe

EN

operator associated with step functions; real and complex B-splines; analytic splines; analytic functions; approximation

• Czasopismo: Opuscula Mathematica
• Rocznik: 2003
• Tom: Vol. 23
• Strony: 99-115
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Wronicz, Z.

• Faculty of Applied Mathematics, AGH University of Science and Technology, Cracow, Poland,

Bibliografia

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