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On a Direct Uvarov-Chihara Problem and Some Extensions

In: Analytic Number Theory, Approximation Theory, and Special Functions

Author

Listed:
  • K. Castillo

    (Universidade Estadual Paulista – UNESP)

  • L. Garza

    (Universidad de Colima)

  • F. Marcellán

    (Universidad Carlos III de Madrid)

Abstract

In this paper, we analyze a perturbation of a nontrivial probability measure dμ supported on an infinite subset on the real line, which consists on the addition of a time-dependent mass point. For the associated sequence of monic orthogonal polynomials, we study its dynamics with respect to the time parameter. In particular, we determine the time evolution of their zeros in the special case when the measure is semiclassical. We also study the dynamics of the Verblunsky coefficients, i.e., the recurrence relation coefficients of a polynomial sequence, orthogonal with respect to a nontrivial probability measure supported on the unit circle, induced from dμ through the Szegő transformation.

Suggested Citation

  • K. Castillo & L. Garza & F. Marcellán, 2014. "On a Direct Uvarov-Chihara Problem and Some Extensions," Springer Books, in: Gradimir V. Milovanović & Michael Th. Rassias (ed.), Analytic Number Theory, Approximation Theory, and Special Functions, edition 127, pages 691-704, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-0258-3_25
    DOI: 10.1007/978-1-4939-0258-3_25
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