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Can we define Taylor polynomials on algebraic curves?

Volume 118 / 2016

Jean-Paul Calvi, Phung Van Manh Annales Polonici Mathematici 118 (2016), 1-24 MSC: Primary 41A05, 41A63. DOI: 10.4064/ap3996-9-2016 Published online: 10 October 2016


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.


  • Jean-Paul CalviInstitut de Mathématiques
    Université de Toulouse III
    CNRS (UMR 5219)
    31062, Toulouse Cedex 9, France
  • Phung Van ManhHanoi National University of Education
    136 Xuan Thuy street
    Cau Giay, Hanoi, Vietnam

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