Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43968
Title: Zeros of Orthogonal Polynomials Generated by the Geronimus Perturbation of Measures
Authors: Branquinho, Amílcar 
Huertas, Edmundo J. 
Rafaeli, Fernando R. 
Issue Date: 2014
Publisher: Springer
Project: info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT 
Serial title, monograph or event: Lecture Notes in Computer Science
Volume: 8579
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)− 1dμ(x) + Nδ(x − c), for some free parameter N∈IR+ 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.
URI: http://hdl.handle.net/10316/43968
Other Identifiers: 10.1007/978-3-319-09144-0_4
DOI: 10.1007/978-3-319-09144-0_4
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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