Results 61 to 70 of about 2,394 (105)
Symmetry, Integrability and Geometry: Methods and Applications, 2008 This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established.
Tom H. Koornwinder
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Spectral Analysis of Certain Schrödinger Operators
Symmetry, Integrability and Geometry: Methods and Applications, 2012 The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators.
Mourad E.H. Ismail, Erik Koelink
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Askey-Wilson Type Functions, With Bound States
, 2003 The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful ...
A. Kasman +36 more
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Tridiagonal Symmetries of Models of Nonequilibrium Physics
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We study the boundary symmetries of models of nonequilibrium physics where the steady state behaviour strongly depends on the boundary rates. Within the matrix product state approach to many-body systems the physics is described in terms of matrices ...
Boyka Aneva
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Generalized Bochner theorem: Characterization of the Askey–Wilson polynomials
Journal of Computational and Applied Mathematics, 2008 Assume that there is a set of monic polynomials $P_n(z)$ satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = _n P_n(z(s)), n=0,1,2,..., N$$ where $z(s), A(s), B(s), C(s)$ are some functions of the discrete argument $s$ and $N$ may be either finite or infinite. The irreducibility condition $A(s-1)C(
Vinet, Luc, Zhedanov, Alexei
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Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
Transactions of the American Mathematical Society, 2020 We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This procedure is then extended to obtain multiple Askey--Wilson, multiple continuous dual $q$-Hahn, and multiple Al ...
Nuwacu, Jean Paul, Van Assche, Walter
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Hidden Symmetries of Stochastic Models
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In the matrix product states approach to $n$ species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process.
Boyka Aneva
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A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
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Bivariate Bannai-Ito polynomials
, 2018 A two-variable extension of the Bannai-Ito polynomials is presented. They are obtained via $q\to-1$ limits of the bivariate $q$-Racah and Askey-Wilson orthogonal polynomials introduced by Gasper and Rahman. Their orthogonality relation is obtained. These
Lemay, Jean-Michel, Vinet, Luc
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations
, 1996 The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap coefficients in the positive discrete series representations of the Lie algebra su(1,1) and the Clebsch-Gordan decomposition leads to generalisations of the ...
Koelink, H. T., Van der Jeugt, J.
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