Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas

摘要: When a nontrivial measure µ on the unit circle satisfies symmetry d ( e i 2 π - ź ) = then associated orthogonal polynomials circle, say n , are all real. In this case, in 1986, Delsarte and Genin have shown that two sequences of para-orthogonal { z + * } where 1 / satisfy three term recurrence formulas also explored some further consequences these such as their connections to interval . The same authors, 1988, provided means extend results cover any circle. However, only recently extension with was thoroughly explored, especially from point view chain sequences. main objective present article is provide theory surrounding for As an important application theory, characterization existence integral 0 | w given terms coefficients α Examples justify results.