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Discrete orthogonal polynomials and difference equations of several variables [PDF]
Advances in Mathematics, 2006 minor typos ...
Plamen Iliev, Yuan Xu
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New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials
Mathematics, 2020 A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation ...
Luis E. Garza +2 more
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Polynomials orthogonal with respect to discrete convolution
Journal of Mathematical Analysis and Applications, 1976 AbstractThe concept of “Discrete Convolution Orthogonality” is introduced and investigated. This leads to new orthogonality relations for the Charlier and Meixner polynomials. This in turn leads to bilinear representations for them. We also show that the zeros of a family of convolution orthogonal polynomials are real and simple.
W. A. Al‐Salam, Mourad E. H. Ismail
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Discrete Orthogonal Polynomial Ensembles and the Plancherel Measure [PDF]
The Annals of Mathematics, 2001 38 pages, published ...
Kurt Johansson
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On Generating Orthogonal Polynomials for Discrete Measures
Zeitschrift für Analysis und ihre Anwendungen, 1998 In the present paper, we derive an algorithm for computing the recurrence coefficients of orthogonal polynomials with respect to discrete measures. This means that the support of the measure is a finite set. The algorithm is based oniormulae of Nevai describing the transformation of recurrence coefficients, if we add a point mass to the measure of ...
Hans-Jürgen Fischer
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Differential equations for discrete Jacobi–Sobolev orthogonal polynomials [PDF]
Journal of Spectral Theory, 2015 The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass point at −1 and/or +1.
Antonio J. Dur'an, M. D. Iglesia
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Asymptotics for varying discrete Sobolev orthogonal polynomials
Applied Mathematics and Computation, 2017 We consider a varying discrete Sobolev inner product such as $$(f,g)_S=\int f(x)g(x)d \mu+M_nf^{(j)}(c)g^{(j)}(c),$$ where $\mu$ is a finite positive Borel measure supported on an infinite subset of the real line, $c$ is adequately located on the real axis, $j \geq0,$ and $\{M_n\}_{n\geq0}$ is a sequence of nonnegative real numbers satisfying a very ...
Juan F. Mañas–Mañas +2 more
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Discrete Orthogonal Polynomial Expansions of Averaged Functions
Journal of Mathematical Analysis and Applications, 1995 Abstract Starting from the classical Fourier coefficients of a given function ƒ(x), Boas and Izumi [J. Indian Math. Soc.24 (1960), 191-210] derived an explicit expression for the Fourier coefficients of g(x), or appropriately defined average of ƒ(x). Later, Askey [J. Math. Anal.
Ilse Fischer
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Some discrete d-orthogonal polynomial sets
Journal of Computational and Applied Mathematics, 2003 AbstractIn this paper, we characterize all polynomial sets which are at the same time d-orthogonal and Δω-Appell. The resulting polynomials reduce to Charlier polynomials for (d,ω)=(1,1). Various properties of the obtained polynomials are singled out: generating function, recurrence relation of order d+1 and a difference equation of order d+1.
Youssèf Ben Cheikh, Ali Zaghouani
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Discrete semi-classical orthogonal polynomials: generalized Charlier
Journal of Computational and Applied Mathematics, 2000 AbstractGeneralized Charlier polynomials are introduced as semi-classical orthogonal polynomials of class 1 with one parameter. Main characteristic data are established from the Laguerre–Freud equations generating the coefficients of the recurrence relation satisfied by the polynomials.
Mahouton Norbert Hounkonnou +2 more
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