Geodesic
On operators of interpolation with respect to solutions of a~Cauchy problem and Lagrange--Jacobi polynomials
Izvestiya. Mathematics , Tome 75 (2011) no. 6, pp. 1215-1248

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

We describe classes of continuous functions for which one has pointwise and uniform convergence of certain Lagrange-type operators (constructed from solutions of a Cauchy problem) and the Lagrange–Jacobi interpolation polynomials ${\mathcal L}_n^{(\alpha_{n},\beta_{n})}(F,\cos\theta)$. We also obtain sufficient conditions for the equiconvergence of these interpolation processes.
Keywords: Lagrange operators, sampling theorem, theory of approximation of functions.
Mots-clés : interpolation processes 
@article{IM2_2011_75_6_a5,
     author = {A. Yu. Trynin},
     title = {On operators of interpolation with respect to solutions of {a~Cauchy} problem and {Lagrange--Jacobi} polynomials},
     journal = {Izvestiya. Mathematics },
     pages = {1215--1248},
     publisher = {mathdoc},
     volume = {75},
     number = {6},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_6_a5/}
}
TY  - JOUR
AU  - A. Yu. Trynin
TI  - On operators of interpolation with respect to solutions of a~Cauchy problem and Lagrange--Jacobi polynomials
JO  - Izvestiya. Mathematics 
PY  - 2011
SP  - 1215
EP  - 1248
VL  - 75
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2011_75_6_a5/
LA  - en
ID  - IM2_2011_75_6_a5
ER  - 
%0 Journal Article
%A A. Yu. Trynin
%T On operators of interpolation with respect to solutions of a~Cauchy problem and Lagrange--Jacobi polynomials
%J Izvestiya. Mathematics 
%D 2011
%P 1215-1248
%V 75
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2011_75_6_a5/
%G en
%F IM2_2011_75_6_a5
A. Yu. Trynin. On operators of interpolation with respect to solutions of a~Cauchy problem and Lagrange--Jacobi polynomials. Izvestiya. Mathematics , Tome 75 (2011) no. 6, pp. 1215-1248. http://geodesic.mathdoc.fr/item/IM2_2011_75_6_a5/