Concerning asymptotic behavior for extremal polynomials associated to nondiagonal Sobolev norms
Summary: Let \(\mathbb P\) be the space of polynomials with complex coefficients endowed with a nondiagonal Sobolev norm \(\parallel \cdot \parallel_{W^{1,p}(V \mu)}\), where the matrix \(V\) and the measure \(\mu\) constitute a \(p\)-admissible pair for \(1 \leq p \leq \infty\). We establish the zero location and asymptotic behavior of extremal polynomials associated to \(\parallel \cdot \parallel_{W^{1,p}(V \mu)}\), stating a hypothesis on the matrix \(V\) rather than on the diagonal matrix appearing in its unitary factorization.
asymptotic behavior of extremal polynomials
scientific article; zbMATH DE number 6167910