Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle
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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.References
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Additional Information
- K. Castillo
- Affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
- MR Author ID: 924654
- Email: kenier@mat.uc.pt
- J. Petronilho
- Affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-501 Coimbra, Portugal
- MR Author ID: 345533
- Email: josep@mat.uc.pt
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 3285-3294
- MSC (2010): Primary 15A42
- DOI: https://doi.org/10.1090/proc/14011
- MathSciNet review: 3803655