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We use Kergin and Hakopian interpolants to give some bases for the dual space of bivariate harmonic polynomials.
Nous utilisons les interpolations de Kergin et d'Hakopian pour construire des bases du dual de l'espace des polynômes harmoniques à deux variables.
Van Manh, Phung 1
@article{CRMATH_2017__355_1_28_0, author = {Van Manh, Phung}, title = {On polynomial interpolation of bivariate harmonic polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {28--33}, publisher = {Elsevier}, volume = {355}, number = {1}, year = {2017}, doi = {10.1016/j.crma.2016.11.008}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.11.008/} }
TY - JOUR AU - Van Manh, Phung TI - On polynomial interpolation of bivariate harmonic polynomials JO - Comptes Rendus. Mathématique PY - 2017 SP - 28 EP - 33 VL - 355 IS - 1 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.11.008/ DO - 10.1016/j.crma.2016.11.008 LA - en ID - CRMATH_2017__355_1_28_0 ER -
%0 Journal Article %A Van Manh, Phung %T On polynomial interpolation of bivariate harmonic polynomials %J Comptes Rendus. Mathématique %D 2017 %P 28-33 %V 355 %N 1 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.11.008/ %R 10.1016/j.crma.2016.11.008 %G en %F CRMATH_2017__355_1_28_0
Van Manh, Phung. On polynomial interpolation of bivariate harmonic polynomials. Comptes Rendus. Mathématique, Tome 355 (2017) no. 1, pp. 28-33. doi : 10.1016/j.crma.2016.11.008. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2016.11.008/
[1] Spline Functions and Multivariate Interpolations, Springer-Verlag, 1993
[2] Kergin interpolant at the roots of unity approximate functions, J. Anal. Math., Volume 72 (1997), pp. 203-221
[3] The polynomial projectors that preserve homogeneous differential relations: a new characterization of Kergin interpolation, East J. Approx., Volume 10 (2004), pp. 441-454
[4] Interpolation of harmonic functions bases on Radon projections, Numer. Math., Volume 127 (2014), pp. 423-445
[5] New results on regularity and errors of harmonic interpolation using Radon projections, J. Comput. Appl. Math., Volume 29 (2016), pp. 73-81
[6] Interpolation in minimum seminorm and multivariate B-spline, J. Approx. Theory, Volume 37 (1983), pp. 212-223
[7] Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type, J. Approx. Theory, Volume 34 (1982), pp. 286-305
[8] A constructive approach to Kergin interpolation in : multivariate B-spline and Lagrange interpolation, Rocky Mt. J. Math., Volume 10 (1980), pp. 485-497
[9] On the convergence of Kergin and Hakopian interpolants at Leja sequences for the disk, Acta Math. Hung., Volume 136 (2012), pp. 165-188
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