Results 21 to 30 of about 71,879 (309)

Discrete Orthogonal Polynomial Expansions of Averaged Functions

Journal of Mathematical Analysis and Applications, 1995
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Ilse Fischer
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Discrete orthogonal polynomials on equidistant nodes [PDF]

International Mathematical Forum, 2007
In this paper we give an alternative and, in our opinion, more simple proof for the orthonormal discrete polynomials on a set of equidistant nodes. Such a proof provides a unifying explicit formulation of discrete orthonormal polynomials on an equidistant grid and an explicit formula for the coefficients of the “three-term recurrence relation”. We show
Eisinberg A, FEDELE, Giuseppe
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Gottlieb Polynomials and Their q-Extensions

Mathematics, 2021
Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles.
Esra ErkuŞ-Duman, Junesang Choi
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Eigenvalue Problem for Discrete Jacobi–Sobolev Orthogonal Polynomials

Mathematics, 2020
In this paper, we consider a discrete Sobolev inner product involving the Jacobi weight with a twofold objective. On the one hand, since the orthonormal polynomials with respect to this inner product are eigenfunctions of a certain differential operator,
Juan F. Mañas-Mañas, Juan J. Moreno-Balcázar, Richard Wellman   +2 more
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Discrete Transforms and Orthogonal Polynomials of (Anti)symmetric Multivariate Sine Functions

Entropy, 2018
Sixteen types of the discrete multivariate transforms, induced by the multivariate antisymmetric and symmetric sine functions, are explicitly developed. Provided by the discrete transforms, inherent interpolation methods are formulated.
Adam Brus, Jiří Hrivnák, Lenka Motlochová   +2 more
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Multidimensional Toda Lattices: Continuous and Discrete Time [PDF]

, 2016
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates.
Aptekarev, Alexander I., Derevyagin, Maxim, Miki, Hiroshi, Van Assche, Walter   +3 more
core   +1 more source

Extensions of discrete classical orthogonal polynomials beyond the orthogonality

Journal of Computational and Applied Mathematics, 2009
It is well known that the family of Hahn polynomials $\{h_n^{ , }(x;N)\}_{n\ge 0}$ is orthogonal with respect to a certain weight function up to $N$. In this paper we present a factorization for Hahn polynomials for a degree higher than $N$ and we prove that these polynomials can be characterized by a $ $-Sobolev orthogonality.
Costas-Santos, Roberto S., Sanchez-Lara, J. F.   +1 more
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On Polynomials Orthogonal with Respect to an Inner Product Involving Higher-Order Differences: The Meixner Case

Mathematics, 2022
In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product f,g=⟨uM,fg⟩+λTjf(α)Tjg(α), where uM is the Meixner linear operator, λ∈R+, j∈N, α≤0, and T is the forward difference operator Δ or ...
Roberto S. Costas-Santos, Anier Soria-Lorente, Jean-Marie Vilaire   +2 more
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Zero distributions for discrete orthogonal polynomials

Journal of Computational and Applied Mathematics, 1998
The authors give an overview of the recent work on the distribution of zeros of discrete orthogonal polynomials. The work by \textit{E. A. Rakhmanov} [Mat. Sb. 187, No. 8, 109-124 (1996); English translation in Sb. Math. 187, No. 8, 1213-1228 (1996; Zbl 0873.42014)] is taken as the starting point of the use of a new kind of equilibrium problems in ...
Arno B. J. Kuijlaars, E. A. Rakhmanov
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On a two-dimensional analogue of the Lebesgue function for Fourier-Chebyshov sums [PDF]

E3S Web of Conferences
This article considers the problem of approximating a function of two variables f(x,y) by Fourier sums over Chebyshev polynomials orthogonal on a discrete grid.
Rustanov A.R., Shikhshinatova M.M.
doaj   +1 more source