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Complementary romanovski-routh polynomials: From orthogonal polynomials on the unit circle to coulomb wave functions
(2019-01-01)
We consider properties and applications of a sequence of polynomials Known as complementary RomanovsKi-Routh polynomials (CRR polynomials for short). These polynomials, which follow from the RomanovsKi-Routh polynomials ...
Explicit formulas for OPUC and POPUC associated with measures which are simple modifications of the Lebesgue measure
(2015-11-15)
We consider nontrivial probability measures, obtained as simple modifications of the Lebesgue measure, which include mass points at z=1 and z=i. The orthogonal polynomials, para-orthogonal polynomials and Toeplitz matrices ...
Extreme zeros in a sequence of para-orthogonal polynomials and bounds for the support of the measure
(2018-01-01)
Given a nontrivial Borel measure μ on the unit circle T{double-struck}, the corresponding reproducing (or Christoffel-Darboux) kernels with one of the variables fixed at z = 1 constitute a family of so-called para-orthogonal ...
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. ...
Orthogonal polynomials associated with complementary chain sequences
(2016-07-27)
Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary ...
A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula
(Elsevier B.V., 2014-08-01)
The objective of this manuscript is to study directly the Favard type theorem associated with the three term recurrence formulaRn+1(Z) = [(1 + ic(n+i))z + (1 - ic(n+1))]R-n(z) - 4d(n+1)zR(n-1)(z), n >= 1,with R-0(z) = 1 ...
On an energy-dependent quantum system with solutions in terms of a class of hypergeometric para-orthogonal polynomials on the unit circle
(2020-07-01)
We study an energy-dependent potential related to the Rosen-Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrodinger operator in terms of a class of functions associated to a ...
On a class of biorthogonal polynomials on the unit circle
(2016-06-01)
A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given ...
Orthogonal polynomials on the unit circle: Verblunsky coefficients with some restrictions imposed on a pair of related real sequences
(2018-05-01)
It was shown recently that associated with a pair of real sequences {{cn}n=1∞,{dn}n=1∞}, with {dn}n=1∞ a positive chain sequence, there exists a unique nontrivial probability measure μ on the unit circle. The Verblunsky ...
Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]
(Rocky Mt Math Consortium, 2003-06-01)
We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through ...