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On zeros of paraorthogonal polynomials


Author: Yen Chi Lun
Journal: Proc. Amer. Math. Soc. 147 (2019), 3389-3399
MSC (2010): Primary 30C45; Secondary 26C10
DOI: https://doi.org/10.1090/proc/14359
Published electronically: April 18, 2019
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Abstract: We prove some results concerning the behaviour of zeros of families of paraorthogonal polynomials on the unit circle. We establish an interlacing property of the zeros of some functions related to the paraorthogonal polynomials. Monotonicity with respect to a parameter is also discussed in detail. A Markov type theorem is proved, and the monotonicity is also considered from a spectral point of view.


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Additional Information

Yen Chi Lun
Affiliation: DMAP, IBILCE, UNESP - Universidade Estadual Paulista, 15055-450 São José do Rio Preto, SP, Brazil
Email: yen.chilun@yahoo.com.tw

DOI: https://doi.org/10.1090/proc/14359
Keywords: Paraorthogonal polynomials, zeros, monotonicity
Received by editor(s): April 3, 2018
Received by editor(s) in revised form: August 14, 2018
Published electronically: April 18, 2019
Communicated by: Mourad Ismail
Article copyright: © Copyright 2019 American Mathematical Society