Comptes Rendus
Numerical Analysis
Various characterisations of Extended Chebyshev spaces via blossoms
Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 815-820.

Among all W-spaces (i.e. spaces with nonvanishing Wronskians), extended Cheyshev spaces can be characterised by the existence of either Bernstein bases, or B-spline bases, or Bézier points, or blossoms in the spaces obtained by integration.

Parmi les W-espaces (espaces à Wronskiens sans zéro), les espaces de Chebyshev généralisés se caractérisent par l'existence de bases de Bernstein, ou de points de Bézier, ou de floraisons, ou de bases de B-splines, dans l'espace obtenu par intégration.

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DOI: 10.1016/j.crma.2004.09.031
Marie-Laurence Mazure 1

1 Laboratoire de modélisation et calcul (LMC-IMAG), université Joseph Fourier, BP 53, 38041 Grenoble cedex, France
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Marie-Laurence Mazure. Various characterisations of Extended Chebyshev spaces via blossoms. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 815-820. doi : 10.1016/j.crma.2004.09.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.031/

[1] J.-M. Carnicer; J.-M. Peña Total positivity and optimal bases (M. Gasca; C.A. Micchelli, eds.), Total Positivity and its Applications, Kluwer Academic, 1996, pp. 133-155

[2] S. Karlin; W.J. Studden Tchebycheff Systems, Wiley Interscience, New York, 1966

[3] M.-L. Mazure B-spline bases and osculating flats: one result of H.-P. Seidel revisited, Math. Model. Numer. Anal., Volume 36 (2002), pp. 1177-1186

[4] T.N.T. Goodman; M.-L. Mazure Blossoming beyond extended Chebyshev spaces, J. Approx. Theory, Volume 109 (2001), pp. 48-81

[5] M.-L. Mazure Blossoming: a geometrical approach, Constr. Approx., Volume 22 (1999), pp. 285-304

[6] M.-L. Mazure Blossoms and optimal bases, Adv. Comput. Math., Volume 20 (2004), pp. 177-203

[7] M.-L. Mazure, Chebyshev spaces and Bernstein bases, Constr. Approx., in preparation

[8] M.-L. Mazure; H. Pottmann Tchebycheff curves (M. Gasca; C.A. Micchelli, eds.), Total Positivity and its Applications, Kluwer Academic, 1996, pp. 187-218

[9] H. Pottmann The geometry of Tchebycheffian splines, Comput. Aided Geom. Design, Volume 10 (1993), pp. 181-210

[10] L.L. Schumaker Spline Functions, Wiley Interscience, New York, 1981

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