Sieved para-orthogonal polynomials on the unit circle

Marcellán, Francisco; Ranga, A. Sri

doi:10.1016/j.amc.2014.07.014

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…Proof of these statements are elementary and can be done by induction and by uniqueness of OPUC defined by recurrence relation (1.8). Note that the OPUC with Verblusnky coefficients satisfying condition (4.17) are called the sieved OPUC [8], [10].…”

Section: 17)mentioning

confidence: 99%

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Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials

Zhedanov¹

2021

Preprint

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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 Φ 0 = 1, Φ 1 (z), . . . , Φ N (z) of polynomials (para) orthogonal on the unit circle (POPUC). This set is determined uniquely by the condition Φ 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.

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Section: 17)mentioning

confidence: 99%

“…The case a n = 1 is exceptional but it is important because it leads to a finite system of OPUC sometimes called the para-orthogonal polynomials (POPUC) [10], [11] . Indeed, assume that a i < 1, i = 0, 1, .…”

Section: Introductionmentioning

confidence: 99%

Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials

Zhedanov¹

2021

Preprint

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Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials

Zhedanov

2022

Proc. Amer. Math. Soc.

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The Kronecker polynomial K ( z ) K(z) is a finite product of cyclotomic polynomials C j ( z ) C_j(z) . Any Kronecker polynomial K ( z ) K(z) of degree N + 1 N+1 with simple roots on the unit circle generates a finite set Φ 0 = 1 \Phi _0=1 , Φ 1 ( z ) \Phi _1(z) , …, Φ N ( z ) \Phi _N(z) of polynomials (para) orthogonal on the unit circle (POPUC). This set is determined uniquely by the condition Φ N ( z ) = ( N + 1 ) − 1 K ′ ( z ) \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 ) C_M(z) . Expressions of these polynomials strongly depend on the decomposition of M M into prime factors.

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Sieved para-orthogonal polynomials on the unit circle

Cited by 2 publications

References 26 publications

Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials

Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials

Para-orthogonal polynomials on the unit circle generated by Kronecker polynomials

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