[PDF] Top 20 On differential equations for orthogonal polynomials on the unit circle

... (1) The set of such polynomials (equivalently, the set of such Carath´eodory func- tions) was defined in [3, 4] as the Laguerre-Hahn class on the unit ...example: ... See full document

... symmetric orthogonal polynomials within the interval [−1, ...uses the information con- tained in the relations associated with S n (z) + S n ∗ (z) (or S n (z) −S n ∗ ... See full document

... focus on families of semi-classical orthogonal polynomials in the so-called class one, w 0 /w = C/A, under the restrictions deg(A) ≤ 1, deg(C) = 2, and some of their extensions, through ... See full document

... families on the real line are characterized in terms of second order differential equations with matrix coefficients for vectors involving the orthogonal polynomials and ... See full document

... deformations on orthogonal polynomials appears in a vast list of papers, mainly focusing on orthogonal polynomials related to semi-classical ...Usually, the deformation ... See full document

... fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid ...These equations arise from applying Newton’s second law to fluid motion, together with ... See full document

... of the paper is organized as follows: in Section 2 we show difference-differential equations for Laguerre-Hahn orthogonal polynomials to be used throughout the paper, and we ... See full document

... of orthogonal polynomials are well-known, their study can be placed within the so-called Laguerre-Hahn ...to the semi-classical case, the Laguerre-Hahn class is also closed under ... See full document

... introduce the concept of Laguerre-Hahn class of hermitian functionals on the unit ...in the linear space of Laurent polynomials and F the corresponding Carath´eodory ... See full document

... between orthogonal polynomials associated with positive measures on the real line and L-orthogonal polynomials associated with strong measures of the class S 3 [0, β, ... See full document

... present the basic results concerning hermitian orthogonality on the unit circle which will be used in the forthcoming ...of orthogonal polynomials on ... See full document

... In the present paper our goal is ...results on semi-classical orthogonal polynomials on quadratic lattices, namely, differ- ence equations involving the polynomials ... See full document

... perturbations on the sequences of orthogonal ...of orthogonal polynomials may appear as a re- sult of modifications of semi-classical orthogonal polynomials, for example, ... See full document

... in the study of orthogonal polynomials associated with exponential weights, for example, in the study of the asymptotic, of estimates for the orthogonal ... See full document

... to the analysis of Carath´ eodory functions satisfying this type of differential equations and to the analysis of its correspon- ding sequences of orthogonal polynomials was done ... See full document

... degree polynomials. Unlike the cases of coherency (2) and (3), to study the semi-classical character and to analyze the relation between the measures of orthogonality becomes much more ... See full document

... With the publications of [20] and [21] in the early 20th century, Szeg˝o introduced the orthogonal polynomials on the unit ...results on these ... See full document

... consider the real Szeg˝o polynomials and obtain some relations to certain self inversive orthogonal L-polynomials dened on the unit circle and corresponding ... See full document

... sequence, orthogonal with respect to a hermitian linear functional u that satisfies a functional equation D (Au) = Bu + zHL , where A, B and H are polynomials and L is the Lebesgue functional, in ... See full document

... Sylvester differential equations are introduced in the study of Laguerre-Hahn orthogonal ...Sylvester differential systems are shown to yield representations for the ... See full document