Publication:
Sobolev-type orthogonal polynomials on the unit circle

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/6068
ISSN: 0096-3003
DOI: 10.1016/S0096-3003(01)00079-0
Files
sobolev_marcellan_amc_2002_ps.pdf (1.21 MB)
Publication date
2002-05-25
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
This paper deals with polynomials orthogonal with respect to a Sobolev-type inner product $$ \langle f,g\rangle =\int_{-\pi}^\pi f(e^{i\theta}) \overline{g(e^{i\theta})} d\mu(e^{i\theta})\, + \, \bold{f}(c)A (\bold{g}(c))^H.$$ where μ is a positive Borel measure supported on [−π,π), A is a nonsingular matrix and 1. We denote f(c)=(f(c),f'(c),\dots,f^{(p)}(c)) and v^H the transposed conjugate of the vector v. We establish the connection of such polynomials with orthogonal polynomials on the unit circle with respect to the measure [see attached full-text file]. Finally, we deduce the relative asymptotics for both families of orthogonal polynomials.
Description
35 pages, no figures.-- MSC2000 codes: 42C05.
MR#: MR1891026 (2003e:42037)
Zbl#: Zbl 1033.42025
Keywords
Orthogonal polynomials, Reflection parameters, Nevai class, Sobolev inner products
Bibliographic citation
Applied Mathematics and Computation, 2002, vol. 128, n. 2-3, p. 329-363
Collections
DM - GAMA - Artículos de Revistas