论文信息 - A new proof of an identity of Jetter and Stöckler for multivariate Bernstein polynomials

A new proof of an identity of Jetter and Stöckler for multivariate Bernstein polynomials

A simple proof of an elegant identity for multivariate Bernstein polynomials discovered recently by K. Jetter and J. Stockler is given. This identity shows a pointwise orthogonality relation of multivariate Bernstein polynomials and implies a new representation for the dual basis of multivariate Bernstein polynomials. Our method is based on "generating functions", which reveals a general structure of the identity.

Ulrich Abel | Zhongkai Li

[1] Kurt Jetter,et al. An identity for multivariate Bernstein polynomials , 2003, Comput. Aided Geom. Des..

[2] P. Sablonnière. Representation of quasi-interpolants as differential operators and applications , 1999 .

[3] Elena E. Berdysheva,et al. New polynomial preserving operators on simplices: direct results , 2004, J. Approx. Theory.

[4] Z. Ciesielski,et al. The degenerate B-splines as a basis in the space of algebraic polynomials , 1985 .

[5] Martin D. Buhmann,et al. New Developments in Approximation Theory , 1999 .

[6] Paul Sablonnière. Bernstein-Type Quasi-Interpolants , 1991, Curves and Surfaces.

[7] Kang Zhao,et al. Dual bases of multivariate Bernstein-Bézier polynomials , 1988, Comput. Aided Geom. Des..

[8] Bert Jüttler,et al. The dual basis functions for the Bernstein polynomials , 1998, Adv. Comput. Math..