A study of the generalized Christoffel functions with applications
The authors investigate the following minimization problem: Let \(f_1,f_2,\ldots,f_m\) be \(m\) linear functionals defined for polynomials and \(m \leq n\). Find the minimum of the quadratic form \(\|P\|^2 = \int_0^{2\pi} |P(e^{i\theta})|^2 d\mu(\theta)\) among all polynomials \(P\) of degree at most \(n\) for which \(f_1(P)=a_1, f_2(P)=a_2,\dots,f_m(P)=a_m\), where \(a_1,\ldots,a_m\) are given complex numbers. First they handle the case when \(m=1\) and then they give the solution for general \(m \leq n\) in terms of determinants containing the solutions with \(m=1\).
scientific article; zbMATH DE number 1513199