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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 ...
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 ...
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 ...
Szego{double acute} and para-orthogonal polynomials on the real line: Zeros and canonical spectral transformations
(2012-08-03)
We study polynomials which satisfy the same recurrence relation as the Szego{double acute} polynomials, however, with the restriction that the (reflection) coefficients in the recurrence are larger than one in modulus. ...
Modified Chebyshev algorithm: some applications
(Springer, 2006-01-01)
Two applications of the modified Chebyshev algorithm are considered. The first application deals with the generation of orthogonal polynomials associated with a weight function having singularities on or near the end points ...