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

T.R. Bіkkuzhyna; V.L. Velikіn

doi:10.15421/241402

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

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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) doi:10.1070/IM1973v007n01ABEH001931

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

Velikin V.L. "Exact values and bounds of interpolational spreads of certain subspaces of Hermitian splines", Res. Math., 2009; 17: pp. 42-47. (in Russian)

Velikin V.L. "On mutual deviation of certain subspaces of interpolational Hermitian splines", Res. Math., 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", Res. Math., 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)