Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality
The authors ``study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form \(e^{-\varphi(x)}\), giving a unified treatment for the so-called Freud (i.e., when \(\varphi\) has polynomial growth at infinity) and Erdös (when \(\varphi\) grows faster than any polynomial at infinity) cases''.
scientific article; zbMATH DE number 5313900