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Strong asymptotics inside the unit disk for Sobolev orthogonal polynomials

✍ Scribed by E. Berriochoa; A. Cachafeiro

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
412 KB
Volume
44
Category
Article
ISSN
0898-1221

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✦ Synopsis

In the present paper, we give sufficient conditions in order to establish the extension of the strong asymptotics up to the boundary and inside the unit disk for Sobolev orthogonal polynomials.

We consider the following Sobolev inner product on the unit circle:

with tt0 a finite positive Borel measure on [0, 2~r] and /xl a measure in the Szeg6's class. On the assumption that the Carath4odory function of #0 and the Szeg6 function of tO have analytic extension, we prove that the asymptotic formula holds true outside the disk and it can be extended inside the disk.

πŸ“œ SIMILAR VOLUMES

Asymptotic Behavior of Sobolev-Type Orth
Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on the Unit Circle
✍ Ana FoulquiΓ© Moreno; Francisco MarcellΓ‘n; K. Pan πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 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