Cita:
Journal of Mathematical Analysis and Applications, 2015, v. 427, Issue 1, pp. 469-483
ISSN:
0022-247X
DOI:
10.1016/j.jmaa.2015.02.063
Agradecimientos:
The authors thank the referee for constructive comments and recommendations which improved the readability and quality of the manuscript. The research of the first author is supported by the Portuguese Government through the Fundação para a Ciência e a Tecnologia (FCT) under the grant SFRH/BPD/ 101139/2014. This author also acknowledges the financial support by the Brazilian Government through the CNPq under the project 470019/2013-1. The research of the first and second author is supported by the Dirección General de Investigación Científica y Técnica, Ministerio de Economía y Competitividad of Spain under the project MTM2012-36732-C03-01. The second author also acknowledges the financial support by the Brazilian Government through the CAPES under the project 107/2012.
In this paper, we study new algebraic and analytic aspects of orthogonal polynomials on the real line when finite modifications of the recurrence coefficients, the so-called co-polynomials on the real line, are considered. We investigate the behavior of their In this paper, we study new algebraic and analytic aspects of orthogonal polynomials on the real line when finite modifications of the recurrence coefficients, the so-called co-polynomials on the real line, are considered. We investigate the behavior of their zeros, mainly interlacing and monotonicity properties. Furthermore, using a transfer matrix approach we obtain new structural relations, combining theoretical and computational advantages. Finally, a connection with the theory of orthogonal polynomials on the unit circle is pointed out.[+][-]