Open Access
Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula : (prepublication)
T.H. Koornwinder
- pp 1-16
About:
The article was published on 1976-01-01 and is currently open access. It has received 58 citations till now. The article focuses on the topics: Orthogonal polynomials & Mehler–Heine formula.read more
Citations
More filters
Book ChapterDOI
Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups
TL;DR: A Jacobi function is defined as a even C∞-function on ℝ which equals 1 at 0 and which satisfies the differential equation as mentioned in this paper, where the Jacobi functions are defined as functions that satisfy the even C ∞-approximation.
Journal ArticleDOI
Linear programming bounds for codes in grassmannian spaces
TL;DR: A bound and its asymptotic version that generalize the well-known bound for codes in the real projective space obtained by Kabatyanskiy and Levenshtein and improve the Hamming bound for sufficiently large minimal distances is obtained.
Journal ArticleDOI
A Non-Negative Representation of the Linearization Coefficients of the Product of Jacobi Polynomials
TL;DR: The problem of linearizing products of orthogonal polynomials, in general, and of ultraspherical and Jacobi poynomials in particular, has been studied by several authors in recent years as mentioned in this paper.
Journal ArticleDOI
Codes and designs in Grassmannian spaces
TL;DR: A notion of f-code in Grassmannian spaces, for which upper bounds are obtained, as well as a kind of duality tight-designs/tight-codes are introduced.
References
More filters
Posted Content
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek,René F. Swarttouw +1 more
TL;DR: The Askey-scheme of hypergeometric orthogonal polynomials was introduced in this paper, where the q-analogues of the polynomial classes in the Askey scheme are given.
Book ChapterDOI
Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups
TL;DR: A Jacobi function is defined as a even C∞-function on ℝ which equals 1 at 0 and which satisfies the differential equation as mentioned in this paper, where the Jacobi functions are defined as functions that satisfy the even C ∞-approximation.
Journal ArticleDOI
Linear programming bounds for codes in grassmannian spaces
TL;DR: A bound and its asymptotic version that generalize the well-known bound for codes in the real projective space obtained by Kabatyanskiy and Levenshtein and improve the Hamming bound for sufficiently large minimal distances is obtained.
Journal ArticleDOI
Jacobi functions: The addition formula and the positivity of the dual convolution structure
TL;DR: In this paper, it was shown that the product of two Jacobi functions of the same argument has a nonnegative Fourier-Jacobi transform, which implies that the convolution structure associated to the inverse Fourier Jacobi transform is positive.
Related Papers (5)
Linearization and connection coefficients of orthogonal polynomials
Ryszard Szwarc,Ryszard Szwarc +1 more