Results 11 to 20 of about 324,599 (288)
Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices [PDF]
, 2000 We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number.
Дмитрий Александрович Лейтес +1 more
openalex +3 more sources
Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (
Hiroshi Miki +2 more
doaj +2 more sources
A Probablistic Origin for a New Class of Bivariate Polynomials [PDF]
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
doaj +3 more sources
Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel [PDF]
arXiv, 2005 For orthogonal polynomials defined by compact Jacobi matrix with exponential decay of the coefficients, precise properties of orthogonality measure is determined. This allows showing uniform boundedness of partial sums of orthogonal expansions with respect to $L^\infty$ norm, which generalize analogous results obtained for little $q$-Legendre, little ...
Josef Obermaier, Ryszard Szwarc
arxiv +3 more sources
Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential ...
G. Filipuk, W. Assche
semanticscholar +5 more sources
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 +2 more
doaj +2 more sources
Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles [PDF]
, 2007 H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials (H. Widom. J. Stat. Phys. 94, (1999) 347-363). We obtain similar results for discrete ensembles whose weights have rational discrete logarithmic derivatives, and compute explicitly correlation kernels ...
Borodin, Alexei, Strahov, Eugene
arxiv +5 more sources
Continuum discretization using orthogonal polynomials [PDF]
Physical Review A, 2003 A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems.
F. Pérez‐Bernal +3 more
openalex +5 more sources
Semi-classical Laguerre polynomials and a third order discrete integrable equation [PDF]
, 2009 A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is a semi-classical Laguerre weight to derive a third order difference equation with a corresponding ...
Christoffel E B +12 more
arxiv +5 more sources
Discrete semiclassical orthogonal polynomials of class 2 [PDF]
arXiv, 2019 In this contribution, discrete semiclassical orthogonal polynomials of class $s\leq2$ are studied. By considering all possible solutions of the Pearson equation, we obtain the canonical families in each class. We also consider limit relations between these and other families of orthogonal polynomials.
Diego Dominici +1 more
arxiv +2 more sources