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.
|Number of pages||16|
|Journal||Electronic Transactions on Numerical Analysis|
|Publication status||Published - 2009|
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