2014/01/01 by Amílcar Branquinho, Edmundo J. Huertas, Fernando R. Rafaeli
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Computer science #Logarithm #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Measure (data warehouse) #Monic polynomial #Orthogonal polynomials #Polynomial #Pure mathematics #Quantum chaos and dynamical systems #math.CA #msc:30C15
paper · pdf · doi:10.1007/978-3-319-09144-0_4
Some minor typos in the text have been corrected. B. Murgante et al. (Eds.): ICCSA 2014 - Lecture Notes in Computer Science (LNCS), 8579 (Part I) (2014), 44-59. Springer International Publishing Switzerland. ISSN 0302-9743. ISBN13: 978-3-319-09143-3. ISBN10: 3-319-09143-3
openalex publication_date 2014/01/01 · arxiv created 2016/02/15 · arxiv updated 2016/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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., (1)/((x-c))dμ(x)+Nδ(x-c), for some free parameter N ∈ 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 of the support of μ.