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Interpolation properties of generalized perfect splines and the solutions of certain extremal problems. I. (English) Zbl 0303.41011


MSC:

41A15 Spline approximation
41A05 Interpolation in approximation theory
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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[1] S. D. Fisher and J. W. Jerome, Perfect spline solutions to \( {L^\infty }\) extremal problems (preprint). · Zbl 0292.49021
[2] G. Glaeser, Prolongement extrémal de fonctions différentiables d’une variable, J. Approximation Theory 8 (1973), 249 – 261 (French). Collection of articles dedicated to Isaac Jacob Schoenberg on his 70th birthday, III. · Zbl 0259.41011
[3] Samuel Karlin, Total positivity. Vol. I, Stanford University Press, Stanford, Calif, 1968.
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[5] Samuel Karlin, Some variational problems on certain Sobolev spaces and perfect splines, Bull. Amer. Math. Soc. 79 (1973), 124 – 128. · Zbl 0253.41010
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[9] R. Louboutin, Sur une bonne partition de l’unite. Appeared in Le prolongateur de Whitney. Vol. II; Ed. Glaeser, Univ. of Rennes, 1967.
[10] I. J. Schoenberg, The perfect \?-splines and a time-optimal control problem, Israel J. Math. 10 (1971), 261 – 274. · Zbl 0273.41006
[11] I. J. Schoenberg and A. Cavaretta, Solution of Landau’s problem concerning higher derivatives on the half line, Report No. 1050, M.R.C., University of Wisconsin, Madison, Wis., 1970. · Zbl 0229.41004
[12] V. M. Tihomirov, Best methods of approximation and interpolation of differentiable functions in the space \?[-1,1]., Mat. Sb. (N.S.) 80 (122) (1969), 290 – 304 (Russian). · Zbl 0204.13301
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