Geodesic
Laurent polynomial perturbations of linear functionals. An inverse problem
Electronic transactions on numerical analysis, Tome 36 (2010)
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},
     year = {2010},
     volume = {36},
     zbl = {1191.42012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2010__36__a6/}
}
TY  - JOUR
AU  - Castillo,  Kenier
AU  - Garza,  Luis
AU  - Marcellán,  Francisco
TI  - Laurent polynomial perturbations of linear functionals. An inverse problem
JO  - Electronic transactions on numerical analysis
PY  - 2010
VL  - 36
UR  - http://geodesic.mathdoc.fr/item/ETNA_2010__36__a6/
LA  - en
ID  - ETNA_2010__36__a6
ER  - 
%0 Journal Article
%A Castillo,  Kenier
%A Garza,  Luis
%A Marcellán,  Francisco
%T Laurent polynomial perturbations of linear functionals. An inverse problem
%J Electronic transactions on numerical analysis
%D 2010
%V 36
%U http://geodesic.mathdoc.fr/item/ETNA_2010__36__a6/
%G en
%F ETNA_2010__36__a6
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/