| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Almeria, Dept Matemat, Almeria 04120 - Spain
[2] Granada Univ, Inst Carlos Fis Teor & Computac 1, Granada - Spain
[3] Univ Estadual Paulista, UNESP, IBILCE, Dept Matemat Aplicada, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[4] Univ Fed Triangulo Mineiro, ICTE, BR-38064200 Uberaba, MG - Brazil
Total Affiliations: 4
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| Document type: | Journal article |
| Source: | Mathematics of Computation; v. 87, n. 309, p. 261-288, JAN 2018. |
| Web of Science Citations: | 3 |
| Abstract | |
Given a nontrivial Borel measure mu on the unit circle T, the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at z = 1 constitute a family of so-called para-orthogonal polynomials, whose zeros belong to T. With a proper normalization they satisfy a three-term recurrence relation determined by two sequences of real coefficients, [c(n)] and [d(n)], where [d(n)] is additionally a positive chain sequence. Coefficients (c(n), d(n)) provide a parametrization of a family of measures related to mu by addition of a mass point at z = 1. In this paper we estimate the location of the extreme zeros (those closest to z = 1) of the para-orthogonal polynomials from the (c(n), d(n))-parametrization of the measure, and use this information to establish sufficient conditions for the existence of a gap in the support of mu at z = 1. These results are easily reformulated in order to find gaps in the support of mu at any other z epsilon T. We provide also some examples showing that the bounds are tight and illustrate their computational applications. (AU) | |
| FAPESP's process: | 09/13832-9 - Orthogonal polynomials, special functions and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |