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Orthogonal polynomials with respect to a family of Sobolev inner products on the unit circle
(2016-03-01)
The principal objective here is to look at some algebraic properties of the orthogonal polynomials Ψn (b,s,t) n with respect to the Sobolev inner product on the unit circle <f,g>S (b,s,t) = (1 − t) <f,g>μ(b) + t f(1) g(1) ...
Sieved para-orthogonal polynomials on the unit circle
(Elsevier B.V., 2014-10-01)
Sieved orthogonal polynomials on the unit circle were introduced independently by Ismail and Li (1992) [15] and Marcellan and Sansigre (1991) [19]. We look at the para-orthogonal polynomials, chain sequences and quadrature ...
A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
(2021-08-01)
This paper deals with orthogonal polynomials and associated connection coefficients with respect to a class of Sobolev inner products on the unit circle. Under certain conditions on the parameters in the inner product it ...
Sieved para-orthogonal polynomials on the unit circle
(Elsevier B.V., 2015)
Complementary Romanovski–Routh Polynomials, Orthogonal Polynomials on the Unit Circle, and Extended Coulomb Wave Functions
(2020-03-01)
In a recent paper (Martínez-Finkelshtein et al. in Proc Am Math Soc 147:2625–2640, 2019) some interesting results were obtained concerning complementary Romanovski–Routh polynomials, a class of orthogonal polynomials on ...
Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas
(2016-11-01)
When a nontrivial measure μ on the unit circle satisfies the symmetry dμ(ei(2π-θ))=-dμ(eiθ) then the associated orthogonal polynomials on the unit circle, say Φn, are all real. In this case, in 1986, Delsarte and Genin ...
Para-orthogonal polynomials from constant Verblunsky coefficients
(Elsevier B.V., 2015-06-15)
Orthogonal polynomials on the unit circle associated with constant Verblunsky coefficients are also known as Geronimus polynomials. We consider the properties of some special sequences of para-orthogonal polynomials that ...
Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind
(2017-06-01)
We refer to a pair of non trivial probability measures (μ0, μ1) supported on the unit circle as a coherent pair of measures of the second kind on the unit circle if the corresponding sequences of monic orthogonal polynomials ...
A modified least squares method: Approximations on the unit circle and on (−1,1)
(2022-08-15)
The main objective in the present manuscript is to consider approximations of functions defined on the unit circle by Laurent polynomials derived from certain combinations of kernel polynomials of orthogonal polynomials ...
A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas
(2013-01-01)
The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the ...