Nested sequences of Chebyshev spaces and shape parameters
ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 6, pp. 773-788. 
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     author = {Mazure, Marie-Laurence and Laurent, Pierre-Jean},
     title = {Nested sequences of {Chebyshev} spaces and shape parameters},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {773--788},
     publisher = {Elsevier},
     volume = {32},
     number = {6},
     year = {1998},
     mrnumber = {1652613},
     zbl = {0922.65010},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1998__32_6_773_0/}
}
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Mazure, Marie-Laurence; Laurent, Pierre-Jean. Nested sequences of Chebyshev spaces and shape parameters. ESAIM: Modélisation mathématique et analyse numérique, Tome 32 (1998) no. 6, pp. 773-788. http://www.numdam.org/item/M2AN_1998__32_6_773_0/

[1] P. J. Barry, de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves, Constructive Approximation 12 (1996), 385-408. | MR | Zbl

[2] P. J. Barry, N. Dyn, R. N. Goldman and C. A. Micchelli, Identities for piecewise polynomial spaces determined by connection matrices, Aequationes Mathematicae 42 (1991), 123-136. | MR | Zbl

[3] D. Bister and H. Prautzsch, A new approach to Tchebycheffian B-splines, in Curves and Surfaces with Applications to CAGD, Vanderbilt University Press (1997), 35-42. | MR | Zbl

[4] N. Dyn, A. Edelman and C. A. Michelli, On locally supported basis functions for the representation of geometrically continuous curves, Analysis 7 (1987), 313-341. | MR | Zbl

[5] N. Dyn and A. Ron, Recurrence relations for Tchebycheffian B-splines, Journal d'Analyse Mathématique 51 (1988), 118-138. | MR | Zbl

[6] S. Karlin, Total Positivity, Stanford University Press, Stanford, 1968. | MR | Zbl

[7] S. Karlin and W. J. Studden, Tchebycheff Systems, Wiley Interscience, New York, 1966. | MR | Zbl

[8] S. Karlin and Z. Ziegler, Chebyshevian spline functions, SIAM Journal Numerical Analysis 3 (1966), 514-543. | MR | Zbl

[9] R. Kulkarni and P.-J. Laurent, Q-splines, Numerical Algorithms 1 (1991), 45-74. | MR | Zbl

[10] R. Kulkarni, P.-J. Laurent and M.-L. Mazure, Non affine blossoms and subdivision for Q-splines, in Math. Methods in Computer Aided Geometric Design II, Academic Press, New York, 1992, 367-380. | MR

[11] P.-J. Laurent, M.-L. Mazure and V. T. Maxim, Chebyshev splines and shape parameters, RR 980M IMAG, Université Joseph Fourier, Grenoble, September 1997, Numerical Algorithms 15 (1997), 373-383. | MR | Zbl

[12] P.-J. Laurent, M.-L. Mazure and G. Morin, Shape effects with polynomial Chebyshev splines, in Curves and Surfaces with Applications in CAGD, Vanderbilt University Press, 1997, 255-262. | MR | Zbl

[13] T. Lyche, A recurrence relation for Chebyshevian B-splines, Constructive Approximation 1 (1985), 155-173. | MR | Zbl

[14] M.-L. Mazure, Blossoming of Chebyshev splines, In Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, 1995, 355-364. | MR | Zbl

[15] M.-L. Mazure, Chebyshev spaces, RR 952M IMAG, Université Joseph Fourier, Grenoble, January 1996.

[16] M.-L. Mazure, Chebyshev blossoming, RR 953M IMAG, Université Joseph Fourier, Grenoble, January 1996.

[17] M.-L. Mazure, Blossoming: a geometric approach, RR 968M IMAG, Université Joseph Fourier, Grenoble, January 1997, to appear in Constructive Approximation. | MR | Zbl

[18] M.-L. Mazure, Vandermonde type determinants and blossoming, The Fourth International Conference on Mathematical Methods for Curves and Surfaces, Lillehammer, Norway, July 3-8, 1997, RR 979M IMAG, Université Joseph Fourier, Grenoble, September 1997, Advances in Computational Math. 8 (1998), 291-315. | MR | Zbl

[19] M.-L. Mazure and P.-J. Laurent, Affine and non affine blossoms, in Computational Geometry, World Scientific, 1993, 201-230. | MR

[20] M.-L. Mazure and P.-J. Laurent, Marsden identities, blossoming and de Boor-Fix formula, in Advanced Topics in Multivariate Approximation, World Scientific Pub., 1996, 227-242. | MR

[21] M.-L. Mazure and P.-J. Laurent, Piecewise smooth spaces in duality: application to blossoming, RR696-M, IMAG, Université Joseph Fourier, Grenoble, January 1997, to appear in Journal of Approximation Theory. | MR | Zbl

[22] M.-L. Mazure and P.-J. Laurent, Polynomial Chebyshev Splines, to appear. | MR | Zbl

[23] M.-L. Mazure and H. Pottmann, Tchebycheff curves, in Total Positivity and its Applications, Kluwer Academic Pub. (1996), 187-218. | MR | Zbl

[24] C. A. Micchelli, Mathematical Aspects of Geometric Modeling, CBMS-NSF Regional Conference Series in Applied Math. 65, SIAM, Philadelphie, 1995. | MR | Zbl

[25] H. Pottmann, The geometry of Tchebycheffian splines, Computer Aided Geometric Design 10 (1993), 181-210. | MR | Zbl

[26] H. Pottmann and M. G. Wagner, Helix splines as an example of affine Tchebycheffian splines, Advances in Computational Math. 2 (1994), 123-142. | MR | Zbl

[27] L. Ramshaw, Blossoms are polar forms, Computer Aided Geometric Design 6 (1989), 323-358. | MR | Zbl

[28] L. L. Schumaker, Spline Functions: Basic Theory, Wiley Interscience, New York, 1981. | MR | Zbl

[29] H.-P. Seidel, New algorithms and techniques for Computing with geometrically continuous spline curves of arbitrary degree, Math. Modelling and Numerical Analysis 26 (1992), 149-176. | Numdam | MR | Zbl

[30] M. G. Wagner and H. Pottmann, Symmetric Tchebycheffian B-splines schemes, in Curves and Surfaces in Geometric Design, A. K. Peters, Wellesley, MA, 1994, 483-490. | MR | Zbl