Publication:
On linearly related orthogonal polynomials and their functionals

Thumbnail Image
Identifiers
URI: http://hdl.handle.net/10016/5981
ISSN: 0022-247X
DOI: 10.1016/S0022-247X(03)00565-1
Files
linearly_marcellan_jmaa_2003_ps.pdf (481.14 KB)
Publication date
2003-11
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
Let $\{P_n\}$ be a sequence of polynomials orthogonal with respect a linear functional $u$ and $\{Q_n\}$ a sequence of polynomials defined by $$P_n(x)+s_nP_{n-1}(x)=Q_n(x)+t_nQ_{n-1}(x).$$ We find necessary and sufficient conditions in order to $\{Q_n\}$ be a sequence of polynomials orthogonal with respect to a linear functional $v$. Furthermore, we prove that the relation between these linear functionals is $(x-\tilde a)u=\lambda (x-a)v$. Even more, if $u$ and $v$ are linked in this way we get that $\{P_n\}$ and $\{Q_n\}$ satisfy a formula as above.
Description
13 pages, no figures.-- MSC2000 codes: 42C05.
MR#: MR2010273 (2004i:33014)
Zbl#: Zbl 1029.42014
Keywords
Orthogonal polynomials, Recurrence relations, Linear functionals
Bibliographic citation
Journal of Mathematical Analysis and Applications, 2003, vol. 287, n. 1, p. 307-319
Collections
DM - GAMA - Artículos de Revistas