Cette note établit un lien fondamental entre existence de floraisons dans un espace de splines (à sections dans différents espaces de Chebyshev généralisés et avec matrices de connexion non nécessairement totalement positives) et possibilité d'interpoler au sens d'Hermite sous conditions de Schoenberg–Whitney.
We state and discuss a theorem which links the existence of blossoms in a spline space (with sections in different Extended Chebyshev spaces and with connection matrices which are not necessarily totally positive) with the possibility of Hermite interpolation in its derivative space under Schoenberg–Whitney conditions.
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@article{CRMATH_2007__344_1_65_0, author = {Kayumov, Alexander and Mazure, Marie-Laurence}, title = {Chebyshevian splines: interpolation and blossoms}, journal = {Comptes Rendus. Math\'ematique}, pages = {65--70}, publisher = {Elsevier}, volume = {344}, number = {1}, year = {2007}, doi = {10.1016/j.crma.2006.11.021}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2006.11.021/} }
TY - JOUR AU - Kayumov, Alexander AU - Mazure, Marie-Laurence TI - Chebyshevian splines: interpolation and blossoms JO - Comptes Rendus. Mathématique PY - 2007 SP - 65 EP - 70 VL - 344 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2006.11.021/ DO - 10.1016/j.crma.2006.11.021 LA - en ID - CRMATH_2007__344_1_65_0 ER -
%0 Journal Article %A Kayumov, Alexander %A Mazure, Marie-Laurence %T Chebyshevian splines: interpolation and blossoms %J Comptes Rendus. Mathématique %D 2007 %P 65-70 %V 344 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2006.11.021/ %R 10.1016/j.crma.2006.11.021 %G en %F CRMATH_2007__344_1_65_0
Kayumov, Alexander; Mazure, Marie-Laurence. Chebyshevian splines: interpolation and blossoms. Comptes Rendus. Mathématique, Tome 344 (2007) no. 1, pp. 65-70. doi : 10.1016/j.crma.2006.11.021. http://archive.numdam.org/articles/10.1016/j.crma.2006.11.021/
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