Hermite-Fejér interpolation with boundary conditions for \(\rho\)-normal sets
In his Habilitationsschrift [Universität, Duisburg (1981] \textit{H. B. Knoop} introduced the polynomials \(H_{n,p,q}f\) which are extensions of the Hermite-Fejer interpolating polynomials. These are based on a triangular set of points \(T\subset [-1,1]\) and include boundary conditions at the end points -1,1 and values and first derivatives at all the points. The boundary conditions at -1 and 1 require all derivatives up to order p-1 and q-1 respectively. Following Fejer and Grunwald, the authors introduce an appropriate generalization of normality and call it (p,q) normality and the corresponding notion of (p,q)-\(\rho\) normality for some \(\rho\), \(0<\rho \leq 1\). They show that when the nodes form a (p,q)-\(\rho\) normal set, the polynomials \(H_{n,p,q}f\) have nice convergence behaviour.
scientific article; zbMATH DE number 4214624
scientific article