Zeros of Orthogonal Polynomials Generated by the Geronimus Perturbation of Measures View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2014

AUTHORS

Amílcar Branquinho , Edmundo J. Huertas , Fernando R. Rafaeli

ABSTRACT

This paper deals with monic orthogonal polynomial sequences (MOPS in short) generated by a Geronimus canonical spectral transformation of a positive Borel measure μ, i.e., (x − c)− 1 dμ(x) + Nδ(x − c), for some free parameter \(N\in{\rm{I\!R}}_{+}\) and shift c. We analyze the behavior of the corresponding MOPS. In particular, we obtain such a behavior when the mass N tends to infinity as well as we characterize the precise values of N such the smallest (respectively, the largest) zero of these MOPS is located outside the support of the original measure μ. When μ is semi-classical, we obtain the ladder operators and the second order linear differential equation satisfied by the Geronimus perturbed MOPS, and we also give an electrostatic interpretation of the zero distribution in terms of a logarithmic potential interaction under the action of an external field. We analyze such an equilibrium problem when the mass point of the perturbation c is located outside the support of μ. More... »

PAGES

44-59

Book

TITLE

Computational Science and Its Applications – ICCSA 2014

ISBN

978-3-319-09143-3
978-3-319-09144-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-09144-0_4

DOI

http://dx.doi.org/10.1007/978-3-319-09144-0_4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1038103299


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