Orthogonal polynomials on the unit circle and related studies
Orthogonal and similar polynomials: properties and applications
Ortogonal polynomials on the real line and on the unit circle
| Full text | |
| Author(s): |
Marcellan, F.
;
Ranga, A. Sri
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Results in Mathematics; v. 71, n. 3-4, p. 1127-1149, JUN 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
We refer to a pair of non trivial probability measures (mu(0), mu(1)) supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials [Phi(n)(mu(0); z)] n >= 0 and [Phi(n)(mu(1); z)] n >= 0 satisfy 1/n Phi'(n)(mu(0); z) = Phi(n-1)(mu(1); z) - chi(n)Phi(n-2)(mu(1);z), n >= 2. It turns out that there are more interesting examples of pairs of measures on the unit circle with this latter coherency property than in the case of the standard coherence. The main objective in this contribution is to determine such pairs of measures. The polynomials orthogonal with respect to the Sobolev inner products associated with coherent pairs of measures of the second kind are also studied. (AU) | |
| FAPESP's process: | 16/09906-0 - Harmonic analysis, approximation theory and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |