کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4644834 1632164 2016 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas
چکیده انگلیسی

When a nontrivial measure μ   on the unit circle satisfies the symmetry dμ(ei(2π−θ))=−dμ(eiθ)dμ(ei(2π−θ))=−dμ(eiθ) then the associated orthogonal polynomials on the unit circle, say ΦnΦn, are all real. In this case, in 1986, Delsarte and Genin have shown that the two sequences of para-orthogonal polynomials {zΦn(z)+Φn⁎(z)} and {zΦn(z)−Φn⁎(z)}, where Φn⁎(z)=znΦn(1/z‾)‾, satisfy three term recurrence formulas and have also explored some further consequences of these sequences of polynomials such as their connections to sequences of orthogonal polynomials on the interval [−1,1][−1,1]. The same authors, in 1988, have also provided a means to extend these results to cover any nontrivial measure on the unit circle. However, only recently the extension associated with the para-orthogonal polynomials zΦn(z)−Φn⁎(z) was thoroughly explored, especially from the point of view of three term recurrence and chain sequences. The main objective of the present article is to provide the theory surrounding the extension associated with the para-orthogonal polynomials zΦn(z)+Φn⁎(z) for any nontrivial measure on the unit circle. As an important application of the theory, a characterization for the existence of the integral ∫02π|eiθ−w|−2dμ(eiθ), where w   is such that |w|=1|w|=1, is given in terms of the coefficients αn−1=−Φn(0)‾, n≥1n≥1. Examples are also provided to justify all the results.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 109, November 2016, Pages 19–40
نویسندگان
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