Abstract
Let be a monic orthogonal polynomial sequence on the unit circle. We define recursively a new sequence of polynomials by the following linear combination: , , . In this paper, we give necessary and sufficient conditions in order to make be an orthogonal polynomial sequence too. Moreover, we obtain an explicit representation for the Verblunsky coefficients and in terms of and . Finally, we show the relation between their corresponding Caratheodory functions and their associated linear functionals.
Highlights
We show the relation between their corresponding Caratheodory functions and their associated linear functionals
We denote by Λ span{zk, k ∈ Z} the linear space of Laurent polynomials with complex coefficients and by Λ the dual algebraic space of Λ
It is well known that the regularity of u is a necessary and sufficient condition for the existence of a sequence of orthogonal polynomials on the unit circle
Summary
Departamento de Matematica Aplicada I, E.T.S.I.I., Universidad de Vigo, Campus Lagoas-Marcosende, 36200 Vigo, Spain. Let {Φn} be a monic orthogonal polynomial sequence on the unit circle. We define recursively a new sequence {Ψn} of polynomials by the following linear combination: Ψn z pnΨn−1 z Φn z qnΦn−1 z , pn, qn ∈ C, pnqn / 0. We give necessary and sufficient conditions in order to make {Ψn} be an orthogonal polynomial sequence too. We show the relation between their corresponding Caratheodory functions and their associated linear functionals
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
