On a direct Uvarov-Chihara problem and some extensions

K. Castillo, L. Garza, F. Marcellán*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)


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 Szego transformation.

Original languageEnglish
Title of host publicationAnalytic Number Theory, Approximation Theory, and Special Functions
Subtitle of host publicationIn Honor of Hari M. Srivastava
PublisherSpringer New York
Number of pages14
ISBN (Electronic)9781493902583
ISBN (Print)1493902571, 9781493902576
Publication statusPublished - 1 Nov 2014
Externally publishedYes

Publication series

NameAnalytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava

Bibliographical note

Publisher Copyright:
© 2014 Springer Science+Business Media New York. All rights reserved.

All Science Journal Classification (ASJC) codes

  • General Mathematics


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