Results 71 to 80 of about 109,685 (181)
A connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line [PDF]
, 2002 Szego's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials L, and leads to a new orthogonality structure in the module LxL.
arxiv +1 more source
Upward extension of the Jacobi matrix for orthogonal polynomials [PDF]
arXiv, 1995 Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials. We investigate new orthogonal polynomials by adding to the Jacobi matrix $r$ new rows and columns, so that the original
arxiv
Vector functions for direct analysis of annular wavefront slope data
Results in Optics, 2022 In the aberration analysis of a wavefront over a certain domain, the polynomials that are orthogonal over and represent balanced aberrations for this domain are used.
Virendra N. Mahajan, Eva Acosta
doaj
Ladder operators and differential equations for multiple orthogonal polynomials [PDF]
, 2012 In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend known results for orthogonal polynomials and can be used to derive the differential equations satisfied by multiple orthogonal polynomials.
arxiv +1 more source
Journal of Computational and Applied Mathematics, 1990 AbstractThe following well-known framework will be applied to Hermite-Padé approximants. First the Hermite-Padé-type approximants will be defined. From the error of approximation some supplementary conditions will be fixed in order to obtain Hermite-Padé-forms. Vector orthogonal polynomials will be deduced from these conditions.
André Draux, Abdallah Maanaoui
openaire +2 more sources
On polynomials orthogonal to all powers of a Chebyshev polynomial on a segment [PDF]
arXiv, 2002 In this paper we describe polynomials orthogonal to all powers of a Chebyshev polynomial on a segment.
arxiv
On quasi-orthogonal polynomials [PDF]
Proceedings of the American Mathematical Society, 1961 where the { pn(X) } n??= are the related orthogonal polynomials. We say that two polynomial sets are related if one set is quasi-orthogonal with respect to the interval and distribution of the orthogonality of the other set. Chihara [2 ] gave a necessary form for a recurrence relation for quasi-orthogonal polynomials. It is the purpose of this paper to
openaire +2 more sources
Advances in Mathematics, 1980 AbstractThe problem is to determine all nonnegative measures on the Borel subsets of the complex plane with respect to which all polynomials are square integrable and with respect to which the Newton polynomials form an orthogonal set. The Newton polynomials do not belong to any classical scheme of orthogonal polynomials.
David Trutt, Louis de Branges
openaire +2 more sources
Finite differences and orthogonal polynomials [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1994 : Explicit representations of specific sets of orthogonal polynomials are often not as useful as one would like them to be. However, being able to work with them can be useful.
R. ASKEY
doaj
Orthogonal polynomials and Möbius transformations [PDF]
arXiv, 2019 Given an orthogonal polynomial sequence on the real line, another sequence of polynomials can be found by composing these polynomials with a general M\"obius transformation. In this work, we study the properties of such M\"obius-transformed polynomials. We show that they satisfy an orthogonality relation in given curve of the complex plane with respect
arxiv