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Szego polynomials and the truncated trigonometric moment problem
(Springer, 2006-12-01)
We show how Szego polynomials can be used in the theory of truncated trigonometric moment problem.
SZEGO and PARA-ORTHOGONAL POLYNOMIALS on THE REAL LINE: ZEROS and CANONICAL SPECTRAL TRANSFORMATIONS
(Amer Mathematical Soc, 2012-10-01)
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 ...
Another connection between orthogonal polynomials and L-orthogonal polynomials
(Elsevier B.V., 2007-06-01)
We consider a connection that exists between orthogonal polynomials associated with positive measures on the real line and orthogonal Laurent polynomials associated with strong measures of the class S-3 [0, beta, b]. ...
Szego type polynomials and para-orthogonal polynomials
(Academic Press Inc. Elsevier B.V., 2010-10-01)
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 polynomials: some relations to L-orthogonal and orthogonal polynomials
(Elsevier B.V., 2003-04-01)
We consider the real Szego polynomials and obtain some relations to certain self inversive orthogonal L-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on real intervals. We also ...
SZEGO POLYNOMIALS FROM HYPERGEOMETRIC FUNCTIONS
(Amer Mathematical Soc, 2010-12-01)
Szego polynomials with respect to the weight function w(theta) = e(eta theta)[sin(theta/2)](2 lambda), where eta, lambda is an element of R and lambda > -1/2 are considered. Many of the basic relations associated with these ...
On perturbed Szego recurrences
(Elsevier B.V., 2014-03-15)
The purpose of the present contribution is to investigate the effects of finite modifications of Verblunsky coefficients on Szego recurrences. More precisely, we study the structural relations and the corresponding C-functions ...
Real orthogonal polynomials in frequency analysis
(Amer Mathematical Soc, 2004-01-01)
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 ...
Schur-Szegö composition of entire functions
(2012)
For any pair of algebraic polynomials A(x) = n k=0 n k akxk and B(x) = n k=0 n k bkxk, their Schur-Szego composition is defined by ˝ (A ∗ n B)(x) = n k=0 n k akbkxk. Motivated by some recent results which show that ...
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS
(Amer Mathematical Soc, 2012-06-01)
A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties ...