Some extremal properties of orthogonal polynomials (Q1057411)

In the synthesis of electric filters the following problem occurs. Given a weight function w(x) on the segment [a,b] and a real number p, determine the n-th order polynomial \(f_ n\) such that \(f_ n(p)=1\) and the integral \(\int^{b}_{a}(f_ n(x))^ 2w(x)dx\) is minimized. The authors solve this problem for \(p\leq a\) (p\(\geq b)\) and discuss some applications of their result. Reviewer's remark: The main theorem follows directly from Theorem 3.1.4 and Section 16.2(4) of \textit{G. Szegö}, Orthogonal polynomials (1959; Zbl 0089.275).