Geodesic
Positive-definite splines of special form
Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1771-1800

Voir la notice de l'article provenant de la source Math-Net.Ru

Even positive-definite splines with support in $[-1,1]$ that are equal to real algebraic polynomials on $[0,1]$ are investigated. Examples of such splines are presented. Under consideration are the $e$-splines, which have several extremal properties, and the positive-definite $A$-splines, which have the maximum possible smoothness on $\mathbb R$. An estimate of the approximation by a linear combination of shifts of an $A$-spline is indicated. New relations for the hypergeometric function ${_1F_2}$ are found. 
@article{SM_2002_193_12_a2,
     author = {V. P. Zastavnyi and R. M. Trigub},
     title = {Positive-definite splines of special form},
     journal = {Sbornik. Mathematics},
     pages = {1771--1800},
     publisher = {mathdoc},
     volume = {193},
     number = {12},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_12_a2/}
}
TY  - JOUR
AU  - V. P. Zastavnyi
AU  - R. M. Trigub
TI  - Positive-definite splines of special form
JO  - Sbornik. Mathematics
PY  - 2002
SP  - 1771
EP  - 1800
VL  - 193
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2002_193_12_a2/
LA  - en
ID  - SM_2002_193_12_a2
ER  - 
%0 Journal Article
%A V. P. Zastavnyi
%A R. M. Trigub
%T Positive-definite splines of special form
%J Sbornik. Mathematics
%D 2002
%P 1771-1800
%V 193
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2002_193_12_a2/
%G en
%F SM_2002_193_12_a2
V. P. Zastavnyi; R. M. Trigub. Positive-definite splines of special form. Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1771-1800. http://geodesic.mathdoc.fr/item/SM_2002_193_12_a2/