On co-polynomials on the real line

• Published in: Journal of mathematical analysis and applications Vol. 427; no. 1; pp. 469 - 483
• Main Authors: Castillo, Kenier, Marcellán, Francisco, Rivero, Jorge
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-07-2015
• Subjects: Co-polynomials on the real line; Orthogonal polynomials on the real line; Transfer matrices; Zeros; Zeros; Co-polynomials on the real line; Transfer matrices; Orthogonal polynomials on the real line
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2015.02.063

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.