Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials
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- by Alexei Zhedanov PDF
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Abstract:
The Kronecker polynomial $K(z)$ is a finite product of cyclotomic polynomials $C_j(z)$. Any Kronecker polynomial $K(z)$ of degree $N+1$ with simple roots on the unit circle generates a finite set $\Phi _0=1$, $\Phi _1(z)$, …, $\Phi _N(z)$ of polynomials (para) orthogonal on the unit circle (POPUC). This set is determined uniquely by the condition $\Phi _N(z) = (N+1)^{-1} K’(z)$. Such set can be called the set of Sturmian Kronecker POPUC. We present several new explicit examples of such POPUC. In particular, we define and analyze properties of the Sturmian cyclotomic POPUC generated by the cyclotomic polynomials $C_M(z)$. Expressions of these polynomials strongly depend on the decomposition of $M$ into prime factors.References
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Additional Information
- Alexei Zhedanov
- Affiliation: School of Mathematics, Renmin University of China, Beijing 100872, People’s Republic of China
- MR Author ID: 234560
- Received by editor(s): September 7, 2021
- Received by editor(s) in revised form: October 27, 2021
- Published electronically: March 17, 2022
- Additional Notes: The work was funded by the National Foundation of China (Grant No.11771015).
- Communicated by: Mourad Ismail
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2629-2645
- MSC (2020): Primary 33C47; Secondary 11Z05
- DOI: https://doi.org/10.1090/proc/15915
- MathSciNet review: 4399277