Generalized qd algorithm and Markov-Bernstein inequalities for Jacobi weight
The authors give new upper and lower bounds for the best constant \(M_n\) in the inequality \[ \|p'\|_{L^2(w)}\leq M_n\|p\|_{L^2(w)}, \] where \(\|f\|_{L^2(w)}= \int_{-1}^1 f^2(x)w(x)\,dx\), \(w(x)=(1-x)^\alpha(1+x)^\beta\). The result is obtained by generalization of the qd algorithm for positive definite symmetric band matrix.
scientific article; zbMATH DE number 5598824