RT Conference Proceedings
T1 Zeros of Orthogonal Polynomials Generated by the Geronimus Perturbation of Measures
A1 Branquinho, Amílcar
A1 Huertas Cejudo, Edmundo José
A1 Rafaeli, Fernando R
AB This paper deals with monic orthogonal polynomial sequences(MOPS in short) generated by a Geronimus canonical spectral transformationof 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 behaviorof the corresponding MOPS. In particular, we obtain such a behaviorwhen the mass N tends to infinity as well as we characterize the precisevalues of N such the smallest (respectively, the largest) zero of theseMOPS is located outside the support of the original measure μ. Whenμ is semi-classical, we obtain the ladder operators and the second orderlinear differential equation satisfied by the Geronimus perturbed MOPS,and we also give an electrostatic interpretation of the zero distributionin terms of a logarithmic potential interaction under the action of anexternal field. We analyze such an equilibrium problem when the masspoint of the perturbation c is located outside the support of μ.
PB Springer
SN 978-3-319-09143-3
SN 0302-9743
YR 2014
FD 2014
LK https://hdl.handle.net/10016/23375
UL https://hdl.handle.net/10016/23375
LA eng
NO Proceedings of: 14th International Conference Computational Science and Its Applications (ICCSA 2014). Guimarães, Portugal, June 30 – July 3, 2014
DS e-Archivo
RD 20 may. 2024