Can we define Taylor polynomials on algebraic curves?
Annales Polonici Mathematici, Tome 118 (2016) no. 1, pp. 1-24
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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
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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/}
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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 -
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
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