(1,1)‐Coherent Pairs on the Unit Circle

Luis Garza, Francisco Marcellán and Natalia C. Pinzón-Cortés

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: A pair (𝒰, 𝒱) of Hermitian regular linear functionals on the unit circle is said to be a (1,1)‐coherent pair if their corresponding sequences of monic orthogonal polynomials {ϕn(x)} n≥0 and {ψn(x)} n≥0 satisfy ϕn[1](z)+anϕn-1[1](z)=ψn(z)+bnψn-1(z), an ≠ 0, n ≥ 1, where ϕn[1](z)=ϕn+1′(z)/(n+1). In this contribution, we consider the cases when 𝒰 is the linear functional associated with the Lebesgue and Bernstein‐Szegő measures, respectively, and we obtain a classification of the situations where 𝒱 is associated with either a positive nontrivial measure or its rational spectral transformation.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/307974

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:307974

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().