Volume 44, pp. 271-280, 2015.
On the discrete extension of Markov's theorem on monotonicity of zeros
Kenier Castillo and Fernando R. Rafaeli
Abstract
Motivated by an open problem proposed by M. E. H. Ismail in
his monograph “Classical and quantum orthogonal polynomials in one variable” (Cambridge
University Press, 2005), we study the behavior of zeros of
orthogonal polynomials associated with
a positive measure on
Full Text (PDF) [199 KB], BibTeX
Key words
orthogonal polynomials on the real line, Uvarov's transformation, Markov's theorem, monotonicity of zeros, asymptotic behavior, speed of convergence
AMS subject classifications
33C45, 30C15
Links to the cited ETNA articles
[6] | Vol. 38 (2011), pp. 317-326 K. Driver, A. Jooste, and K. Jordaan: Stieltjes interlacing of zeros of Jacobi polynomials from different sequences |
[7] | Vol. 19 (2005), pp. 37-47 A. Garrido, J. Arvesú, and F. Marcellán: An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials |