Laurent polynomial perturbations of linear functionals. An inverse problem

Kenier Castillo*, Luis Garza, Francisco Marcellán

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Given a linear functional ℒ in the linear space ℙ of polynomials with complex coefficients, we analyze those linear functionals ℒ∼ such that, for a fixed α Ε ℂ, (ℒ∼, (z + z -1 - (α + ᾱ))p) = (ℒ, p) for every p Ε ℙ. We obtain the relation between the corresponding Carathéodory functions in such a way that a linear spectral transform appears. If ℒ is a positive definite linear functional, the necessary and sufficient conditions in order for ℒ∼ to be a quasi-definite linear functional are given. The relation between the corresponding sequences of monic orthogonal polynomials is presented.

Original languageEnglish
Pages (from-to)83-98
Number of pages16
JournalElectronic Transactions on Numerical Analysis
Publication statusPublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis


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