On co-polynomials on the real line Articles uri icon

publication date

  • July 2015

start page

  • 469

end page

  • 483

issue

  • 1

volume

  • 427

international standard serial number (ISSN)

  • 0022-247X

electronic international standard serial number (EISSN)

  • 1096-0813

abstract

  • 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.

keywords

  • orthogonal polynomials on the real line; co-polynomials on the real line; zeros; transfer matrices