Can we define Taylor polynomials on algebraic curves?

Jean-Paul Calvi¹ ; Phung Van Manh²

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

Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 1-24.

Résumé

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.

Détail

DOI : 10.4064/ap3996-9-2016

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