Exact values of mutual deviation of certain interpolation subspaces of Hermitian splines in uniform and integral metric

T.R. Bіkkuzhyna (Oles Honchar Dnipropetrovsk National University)
V.L. Velikіn (Oles Honchar Dnipropetrovsk National University)

Abstract


We obtained exact values of mutual deviation of interpolation subspaces of Hermitian splines of arbitraty orders on the classes of continuous and continuously differentiable functions in $$$L_p$$$ spaces, $$$1 \leqslant p \leqslant \infty$$$.

Keywords


splines; subspace; normed space

References


Velikin V.L. "Exact values of approximation by Hermitian splines on the classes of differentible functions", Izv. AN SSSR, Ser. matematicheskaya, 1973; 37: pp. 165-185. (in Russian)

Velikin V.L., Bovduj E.Yu. "On interpolational spread of certain subspaces of Hermitian splines", Dnipr. Univ. Math. Bull., 2007; 8: pp. 54-56. (in Russian)

Velikin V.L. "Exact values and bounds of interpolational spreads of certain subspaces of Hermitian splines", Dnipr. Univ. Math. Bull., 2009; 17: pp. 54-56. (in Russian)

Velikin V.L. "On mutual deviation of certain subspaces of interpolational Hermitian splines", Dnipr. Univ. Math. Bull., 2010; 18: pp. 14-16. (in Russian)

Velikin V.L. "On mutual deviation of certain subspaces of interpolational Hermitian splines on different nets of knots", Dnipr. Univ. Math. Bull., 2011; 19: pp. 32-40. (in Russian)

Akhiezer N.I., Glazman I.M. Theory of linear operators in Hilbert space, Vyshcha shkola, Kharkov, 1977; Vol. 1: 316 p. (in Russian)


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Copyright (c) 2014 T.R. Bіkkuzhyna, V.L. Velikіn

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