Zeros of orthogonal polynomials generated by canonical perturbations of measures

Zeros of Orthogonal Polynomials Generated by the Geronimus Perturbation of Measures

“…and we obtain the behavior of the zeros {y 0,−1,N n,s } n s=1 as N increases. We enclose in Figure 1 Remark 3 Looking at the external potential (52) there are few significant differences with respect to the Uvarov case (see [14,Sec. 4.2]).…”

“…Following this premise, the purpose of this paper is twofold. First, using a similar approach as was done in [14], we provide a new connection formula for the Geronimus perturbed MOPS, which will be crucial to obtain sharp limits (and the speed of convergence to them) of their zeros. We provide a comprehensive study of the zeros in terms of the free parameter of the perturbation N , which somehow determines how important the perturbation on the classical measure µ is.…”

Uma Extensão do Teorema de Markov

“…são vistas com frequência na literatura (ver [3,5], por exemplo). No trabalho [3] encontramos resultados sobre os zeros de polinômios ortogonais com relação a (16).…”

Ecuaciones Holonómicas Asociadas a Transformaciones Canónicas del Peso Clásico de Laguerre

“…x − ζ x − η , ρ * (x) = (x − ζ 1 )(x − ζ 2 ) y ρ * * (x) = 1 x − η , además ζ, ζ 1 , ζ 2 y η son reales negativos. Estas perturbaciones al peso original son conocidas como transformaciones canónicas de tipo Christoffel o Geronimus, y las familias de polinomios ortogonales asociadas a estas han sido ampliamente estudiadas en las últimas décadas, destacando los trabajos [4], [6], [7], [8], [9], [14] y [15], en esencia, relacionados con comportamiento asintótico y localización de ceros. Es bien sabido que las sucesiones clásicas de polinomios ortogonales satisfacen una ecuación diferencial de la forma…”