Blossoms of generalized derivatives in Chebyshev spaces
The aim of this paper is to extend the classical formulas on the blossoms of the derivative of a several variables polynomial function to the Chebyshev framework. In any extended Chebyshev space it is possible to associate appropriate differential operators which, in this setting, play the same role as the ordinary derivatives in the polynomial space, and which are named ``generalized derivatives''. To define the blossoms in the extended Chebyshev space it is necessary to work in projective spaces. The central result of this paper is Theorem 1, which gives an explicit formula for obtaining the blossoms of the generalized derivative in the \(n\)-dimensional extended Chebyshev space. As applications of this formula, the author gives a formula to obtain the so called Chebyshev-Bézier points of a function and also an iterative differentiation formula for blossoms.
scientific article; zbMATH DE number 2136995