Zero distributions via orthogonality

Laurent Baratchart (1) , R. Küstner , V. Totik

1 APICS - Analysis and Problems of Inverse type in Control and Signal processing

We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We illustrate the procedure in four cases: classical orthogonality, non-Hermitian orthogonality, rational approximation of Markov-type functions and its non-Hermitian variant. In the last three cases, the results are first of this kind.

Mots clés: FUNCTION THEORY; POTENTIAL THEORY; ORTHOGONAL POLYNOMIALS; NON-HERMITIAN ORTHOGONAL POLYNOMIALS; RATIONAL APPROXIMATION; MEROMORPHIC APPROXIMATION

Domaines: Autre [cs.OH]

Laurent Baratchart, R. Küstner, V. Totik. Zero distributions via orthogonality. RR-5291, INRIA. 2004, pp.34. ⟨inria-00070709⟩