An identity for a general class of approximation operators
In \textit{K. Jetter} and \textit{J. Stöckler} [Comput. Aided Geom. Des. 20, No. 8--9, 563--577 (2003; Zbl 1069.41501)] is presented an identity for multivariate Bernstein polynomials on simplices, which may be considered a pointwise orthogonality relation. This univariate form is generalized in the present paper in two directions. Firstly, is allowed the derivatives of the Bernstein basis polynomials to depend on different variables. Secondly, is considered a general class of positive linear approximation operators including the Bernstein operator as a special case, and is proved an identity for the basis functions of that general class of positive linear operators. As application is given a representation of a restricted dual basis and is defined a class of quasi-interpolants.
scientific article; zbMATH DE number 5077949