On new Bézier bases with Schurer polynomials and corresponding results in approximation theory

On multivariate polynomials in Bernstein-Bézier form and tensor algebra

The Bernstein-Bézier representation of polynomials is a very useful tool in computer aided geometric design. In this paper we make use of (multilinear) tensors to describe and manipulate multivariate polynomials in their Bernstein-Bézier form. As application we consider Hermite interpolation with polynomials and splines.

New results in extremal problems with polynomials

In this paper we give some new results in extremal problems with polynomials which are generalization of some results of F. Locher. 2000 Mathematical Subject Classification: 26D15, 65D32 In [6] F. Locher studies some extremal problems for semidefinition polynomials (nenegative or nepositive) with the dominant coefficient equal to 1. For this he uses the quadrature formulae with high algebraical...

Polynomials on Banach Spaces with Unconditional Bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of...

Bernstein-Bézier polynomials on spheres and sphere-like surfaces

In this paper we discuss a natural way to deene barycentric coordinates on general sphere-like surfaces. This leads to a theory of Bernstein-B ezier polynomials which parallels the familiar planar case. Our constructions are based on a study of homogeneous polynomials on trihedra in IR 3. The special case of Bernstein-B ezier polynomials on a sphere is considered in detail.

Some Results on p-Best Approximation in Vector Spaces