Geodesic
Topological Splines in Locally Convex Spaces
Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 857-885

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

In the present paper, we propose a new approximation method in different function spaces. A specific feature of this method is that the choice of the basis approximating elements significantly depends on the topology of the given function space. Basis elements are constructed using the duality theory of locally convex spaces. A method of their exact calculation is presented. The approximating constructions are far-reaching generalizations of the classical Schoenberg splines and, by analogy with the latter, may be called topological splines. In the general case, such a definition of splines is not related to the choice of the grid. In this paper, we give many examples that are useful for practical applications.
Keywords: topological spline, Schoenberg spline, locally convex space, duality theory, topological homomorphism, polar, Radon measure.
Mots-clés : quotient space, Fréchet space 
@article{MZM_2009_85_6_a5,
     author = {A. P. Kolesnikov},
     title = {Topological {Splines} in {Locally} {Convex} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {857--885},
     publisher = {mathdoc},
     volume = {85},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a5/}
}
TY  - JOUR
AU  - A. P. Kolesnikov
TI  - Topological Splines in Locally Convex Spaces
JO  - Matematičeskie zametki
PY  - 2009
SP  - 857
EP  - 885
VL  - 85
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a5/
LA  - ru
ID  - MZM_2009_85_6_a5
ER  - 
%0 Journal Article
%A A. P. Kolesnikov
%T Topological Splines in Locally Convex Spaces
%J Matematičeskie zametki
%D 2009
%P 857-885
%V 85
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a5/
%G ru
%F MZM_2009_85_6_a5
A. P. Kolesnikov. Topological Splines in Locally Convex Spaces. Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 857-885. http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a5/