We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel ...

We study the use of para-orthogonal polynomials in solving the frequency analysis problem. Through a transformation of Delsarte and Genin, we present an approach for the frequency analysis by using the zeros and Christoffel ...

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 ...

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 ...

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) ...

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 ...

Szego type polynomials with respect to a linear functional M for which the moments M[t(n)] = mu(-n) are all complex, mu(-n) = mu(n) and D(n) not equal 0 for n >= 0. are considered. Here, D(n) are the associated Toeplitz ...

Szego type polynomials with respect to a linear functional M for which the moments M[t(n)] = mu(-n) are all complex, mu(-n) = mu(n) and D(n) not equal 0 for n >= 0. are considered. Here, D(n) are the associated Toeplitz ...

We study polynomials which satisfy the same recurrence relation as the Szego polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. Para-orthogonal ...