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Concerning asymptotic behavior for extremal polynomials associated to nondiagonal Sobolev norms. (English) Zbl 1267.41008

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.

MSC:

41A10 Approximation by polynomials
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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