On positivity properties of fundamental cardinal polysplines

H. Render

Geodesic

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On positivity properties of fundamental cardinal polysplines

H. Render

Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Résumé

Polysplines on strips of order $p$ are natural generalizations of univariate splines. In [3] and [4] interpolation results for cardinal polysplines on strips have been proven. In this paper the following problems will be addressed: (i) positivity of the fundamental polyspline on the strip $\left[ -1,1\right] \times {\Bbb R}^{n}$, and (ii) uniqueness of interpolation for polynomially bounded cardinal polysplines.

Zbl

Keywords: Cardinal splines, L-splines, fundamental spline, polyharmonic functions, polysplines

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     author = {H. Render},
     title = {On positivity properties of fundamental cardinal polysplines},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {101 - 114},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2006},
     zbl = {1119.41008},
     url = {http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a8/}
}

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H. Render. On positivity properties of fundamental cardinal polysplines. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1. http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a8/