%0 Journal Article
%T On Linear Combinations of Two Orthogonal Polynomial Sequences on the Unit Circle
%A C. Su&#225
%A rez
%J Advances in Difference Equations
%D 2010
%I Springer
%R 10.1155/2010/406231
%X Let {¦µn} be a monic orthogonal polynomial sequence on the unit circle. We define recursively a new sequence {¦·n} of polynomials by the following linear combination: ¦·n(z)+pn¦·n-1(z)=¦µn(z)+qn¦µn-1(z), pn,qn¡Ê , pnqn¡Ù0. In this paper, we give necessary and sufficient conditions in order to make {¦·n} be an orthogonal polynomial sequence too. Moreover, we obtain an explicit representation for the Verblunsky coefficients {¦µn(0)} and {¦·n(0)} in terms of pn and qn. Finally, we show the relation between their corresponding Carath¨¦odory functions and their associated linear functionals.
%U http://dx.doi.org/10.1155/2010/406231