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Nikolskii type inequality for cardinal splines

Authors:

Gensun Fang

Institution:

(1) Department of Mathematics, Beijing Normal University, 100875 Beijing, China

Abstract:

The Nikolskii type inequality for cardinal splines

$||s||_{p(R)} \leqslant 2(1 + 4\pi )2^{1 - \tfrac{q}{p}} \left( {\frac{\pi }{h}} \right)^{\tfrac{1}{q} - \tfrac{1}{p}} ||s||_{ q(R)} ,0 < q < p \leqslant \infty$

is proved, which is exact in the sense of order, where ∈ ℒ_m,h, and ℒ_m,k is the space of cardinal splines with nodes

$\left\{ {jh + \frac{1}{2}(m - 1)h} \right\}_{j \in z}$

Project supported by the National Natural Science Foundation of China (Grant No. 19671012), and Doctoral Programme Foundation of Institution of Higher Education.

Keywords:

Nikolskii type inequality cardinal splines entire fonctions

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