We study -splines (existence, uniqueness and convergence) in Banach spaces with a view to applications in approximation. Our approach allows, in particular, considering some problems in a more regular domain, and hence facilitating their solution.
@article{bwmeta1.element.bwnjournal-article-smv106i3p203bwm,
author = {N. Benbourhim and J. Gaches},
title = {$T\_{f}$-splines et approximation par $T\_{f}$ -prolongement},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {203-211},
zbl = {0810.41016},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv106i3p203bwm}
}
Benbourhim, N.; Gaches, J. $T_{f}$-splines et approximation par $T_{f}$ -prolongement. Studia Mathematica, Tome 104 (1993) pp. 203-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i3p203bwm/
[00000] [1] M. Attéia, Convergence interne et externe des fonctions spline d'interpolation, Séminaire d'Analyse Numérique de Toulouse, 1975.
[00001] [2] P. G. Ciarlet, Élasticité tridimensionnelle, Masson, Paris 1986.
[00002] [3] J. Deny et J. L. Lions, Les espaces du type de Beppo Levi, Ann. Inst. Fourier 5 (1954), 305-370. | Zbl 0065.09903
[00003] [4] J. Duchon, Splines minimizing rotation-invariant semi-norms in Sobolev spaces, in: Lecture Notes in Math. 571, Springer, 1977, 85-100.
[00004] [5] I. Ekeland et R. Temam, Analyse convexe et problèmes variationnels, Dunod, Paris 1974.
[00005] [6] P. J. Laurentet Pham-Dinh-Tuan, Global approximation of a compact set by elements of a convex set in a normed space, Numer. Math. 15 (1970), 137-150.
[00006] [7] J. Nečas, Les méthodes directes en théorie des équations elliptiques, Hermann, Paris 1972.
[00007] [8] D. V. Pai, On nonlinear minimization problems and Lf-splines, I, J. Approx. Theory 39 (1983), 228-235. | Zbl 0541.41038