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Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle


Authors: K. Castillo and J. Petronilho
Journal: Proc. Amer. Math. Soc. 146 (2018), 3285-3294
MSC (2010): Primary 15A42
DOI: https://doi.org/10.1090/proc/14011
Published electronically: February 28, 2018
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Abstract: The purpose of this note is to extend in a simple and unified way the known results on interlacing of zeros of paraorthogonal polynomials on the unit circle. These polynomials can be regarded as the characteristic polynomials of any matrix similar to a unitary upper Hessenberg matrix with positive subdiagonal elements.


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Additional Information

K. Castillo
Affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
Email: kenier@mat.uc.pt

J. Petronilho
Affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
Email: josep@mat.uc.pt

DOI: https://doi.org/10.1090/proc/14011
Keywords: Paraorthogonal polynomials on the unit circle, zeros, unitary matrices, eigenvalues, interlacing, rank one perturbations.
Received by editor(s): June 13, 2017
Received by editor(s) in revised form: November 2, 2017
Published electronically: February 28, 2018
Communicated by: Mourad Ismail
Article copyright: © Copyright 2018 American Mathematical Society

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