Geodesic
Laurent polynomial perturbations of linear functionals. An inverse problem
Electronic transactions on numerical analysis, Tome 36 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 - $1 \alpha \in C$, L, (z + z - ($\alpha + $###$ \alpha $))p = L, p for every p $\in P$. 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.
Classification : 42C05
Keywords: orthogonal polynomials, linear functionals, Laurent polynomials, linear spectral transformations 
@article{ETNA_2010__36__a6,
     author = {Castillo, Kenier and Garza, Luis and Marcell\'an, Francisco},
     title = {Laurent polynomial perturbations of linear functionals. {An} inverse problem},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {36},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__36__a6/}
}
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Castillo, Kenier; Garza, Luis; Marcellán, Francisco. Laurent polynomial perturbations of linear functionals. An inverse problem. Electronic transactions on numerical analysis, Tome 36 (2010). http://geodesic.mathdoc.fr/item/ETNA_2010__36__a6/