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Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Measures

✍ Scribed by Andrei Martı́nez-Finkelshtein; Juan J Moreno-Balcázar; Teresa E Pérez; Miguel A Piñar

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
332 KB
Volume
92
Category
Article
ISSN
0021-9045

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✦ Synopsis

Strong asymptotics for the sequence of monic polynomials Q n (z), orthogonal with respect to the inner product

with z outside of the support of the measure + 2 , is established under the additional assumption that + 1 and + 2 form a so-called coherent pair with compact support. Moreover, the asymptotic behaviour of the (square of) the norm (Q n , Q n ) S and of the zeros of Q n is obtained.

📜 SIMILAR VOLUMES

Asymptotic Behavior of Sobolev-Type Orth
Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on the Unit Circle
✍ Ana Foulquié Moreno; Francisco Marcellán; K. Pan 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 184 KB

We study the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product on the unit circle is a M\_M positive definite matrix or a positive semidefinite diagonal block matrix, M=l 1 + } } } +l m +m, d+ belongs to a certain class of measures, and