1Institut de Mathématiques Université de Toulouse III CNRS (UMR 5219) 31062, Toulouse Cedex 9, France 2Hanoi National University of Education 136 Xuan Thuy street Cau Giay, Hanoi, Vietnam
Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 1-24
We study the problem of finding the correct definition of a Taylor polynomial of degree $d$ at a point $\mathbf {a}$ for a function defined on an irreducible algebraic curve $V$ in $\mathbb {C}^2$. We show that a satisfactory definition can be given if and only if the point $\mathbf {a}$ is $d$-Taylorian, which holds for all but finitely many points of $V$. We provide an application to the study of the limit of certain Lagrangian interpolation operators when points coalesce.
Keywords:
study problem finding correct definition taylor polynomial degree point mathbf function defined irreducible algebraic curve mathbb satisfactory definition given only point mathbf d taylorian which holds finitely many points nbsp provide application study limit certain lagrangian interpolation operators points coalesce
Affiliations des auteurs :
Jean-Paul Calvi
1
;
Phung Van Manh
2
1
Institut de Mathématiques Université de Toulouse III CNRS (UMR 5219) 31062, Toulouse Cedex 9, France
2
Hanoi National University of Education 136 Xuan Thuy street Cau Giay, Hanoi, Vietnam
@article{10_4064_ap3996_9_2016,
author = {Jean-Paul Calvi and Phung Van Manh},
title = {Can we define {Taylor} polynomials on algebraic curves?},
journal = {Annales Polonici Mathematici},
pages = {1--24},
year = {2016},
volume = {118},
number = {1},
doi = {10.4064/ap3996-9-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap3996-9-2016/}
}
TY - JOUR
AU - Jean-Paul Calvi
AU - Phung Van Manh
TI - Can we define Taylor polynomials on algebraic curves?
JO - Annales Polonici Mathematici
PY - 2016
SP - 1
EP - 24
VL - 118
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/ap3996-9-2016/
DO - 10.4064/ap3996-9-2016
LA - en
ID - 10_4064_ap3996_9_2016
ER -
%0 Journal Article
%A Jean-Paul Calvi
%A Phung Van Manh
%T Can we define Taylor polynomials on algebraic curves?
%J Annales Polonici Mathematici
%D 2016
%P 1-24
%V 118
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/ap3996-9-2016/
%R 10.4064/ap3996-9-2016
%G en
%F 10_4064_ap3996_9_2016
Jean-Paul Calvi; Phung Van Manh. Can we define Taylor polynomials on algebraic curves?. Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 1-24. doi: 10.4064/ap3996-9-2016
