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Sri Ranga, Daniel Veronese, Kenier Castillo, Marisa Costa","submitted_at":"2013-09-04T12:08:07Z","abstract_excerpt":"The objective of this manuscript is to study directly the Favard type theorem associated with the three term recurrence formula % \\[ R_{n+1}(z) = \\big[(1+ic_{n+1})z+(1-ic_{n+1})\\big] R_{n}(z) - 4 d_{n+1} z R_{n-1}(z), \\quad n \\geq 1, \\] % with $R_{0}(z) =1$ and $R_{1}(z) = (1+ic_{1})z+(1-ic_{1})$, where $\\{c_n\\}_{n=1}^{\\infty}$ is a real sequence and $\\{d_n\\}_{n=1}^{\\infty}$ is a positive chain sequence. We establish that there exists an unique nontrivial probability measure $\\mu$ on the unit circle for which $\\{R_n(z) - 2(1-m_n)R_{n-1}(z)\\}$ gives the sequence of orthogonal polynomials. 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Sri Ranga, Daniel Veronese, Kenier Castillo, Marisa Costa","submitted_at":"2013-09-04T12:08:07Z","abstract_excerpt":"The objective of this manuscript is to study directly the Favard type theorem associated with the three term recurrence formula % \\[ R_{n+1}(z) = \\big[(1+ic_{n+1})z+(1-ic_{n+1})\\big] R_{n}(z) - 4 d_{n+1} z R_{n-1}(z), \\quad n \\geq 1, \\] % with $R_{0}(z) =1$ and $R_{1}(z) = (1+ic_{1})z+(1-ic_{1})$, where $\\{c_n\\}_{n=1}^{\\infty}$ is a real sequence and $\\{d_n\\}_{n=1}^{\\infty}$ is a positive chain sequence. We establish that there exists an unique nontrivial probability measure $\\mu$ on the unit circle for which $\\{R_n(z) - 2(1-m_n)R_{n-1}(z)\\}$ gives the sequence of orthogonal polynomials. 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