On a direct Uvarov-Chihara problem and some extensions

K. Castillo; L. Garza; F. Marcellán

doi:10.1007/978-1-4939-0258-3_25

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 proceeding › Chapter

1 Citation (Scopus)

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 Szego transformation.

Original language	English
Title of host publication	Analytic Number Theory, Approximation Theory, and Special Functions
Subtitle of host publication	In Honor of Hari M. Srivastava
Publisher	Springer New York
Pages	691-704
Number of pages	14
Volume	9781493902583
ISBN (Electronic)	9781493902583
ISBN (Print)	1493902571, 9781493902576
DOIs	https://doi.org/10.1007/978-1-4939-0258-3_25
Publication status	Published - 1 Nov 2014
Externally published	Yes

Publication series

Name	Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava
Volume	9781493902583

Bibliographical note

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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/978-1-4939-0258-3_25

Cite this

Castillo, K., Garza, L., & Marcellán, F. (2014). On a direct Uvarov-Chihara problem and some extensions. In Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava (Vol. 9781493902583, pp. 691-704). (Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava; Vol. 9781493902583). Springer New York. https://doi.org/10.1007/978-1-4939-0258-3_25

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Castillo, K, Garza, L & Marcellán, F 2014, On a direct Uvarov-Chihara problem and some extensions. in Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava. vol. 9781493902583, Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava, vol. 9781493902583, Springer New York, pp. 691-704. https://doi.org/10.1007/978-1-4939-0258-3_25

On a direct Uvarov-Chihara problem and some extensions. / Castillo, K.; Garza, L.; Marcellán, F.
Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava. Vol. 9781493902583 Springer New York, 2014. p. 691-704 (Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava; Vol. 9781493902583).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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N2 - 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.

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Castillo K, Garza L, Marcellán F. On a direct Uvarov-Chihara problem and some extensions. In Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava. Vol. 9781493902583. Springer New York. 2014. p. 691-704. (Analytic Number Theory, Approximation Theory, and Special Functions: In Honor of Hari M. Srivastava). doi: 10.1007/978-1-4939-0258-3_25

On a direct Uvarov-Chihara problem and some extensions

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