Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results [PDF]
, 2002 We compute the pointwise asymptotics of orthogonal polynomials with respect to a general class of pure point measures supported on finite sets as both the number of nodes of the measure and also the degree of the orthogonal polynomials become large.
Jinho Baik +3 more
openalex +4 more sources
A discrete orthogonal polynomials approach for fractional optimal control problems with time delay [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2019 An efficient direct and numerical method has been proposed to approximate a solution of time-delay fractional optimal control problems. First, a class of discrete orthogonal polynomials, called Hahn polynomials, has been introduced and their properties ...
F. Mohammadi
doaj +2 more sources
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
doaj +2 more sources
Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials [PDF]
, 2013 The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given as a second ...
Vincenz̊o Aquilanti +2 more
openalex +3 more sources
Solvable discrete quantum mechanics: q-orthogonal polynomials with q=1 and quantum dilogarithm [PDF]
, 2015 Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems.
Satoru Odake, Ryu Sasaki
openalex +6 more sources
Equilibria of ‘discrete’ integrable systems and deformation of classical orthogonal polynomials [PDF]
, 2004 The Ruijsenaars-Schneider systems are `discrete' version of the Calogero-Moser (C-M) systems in the sense that the momentum operator p appears in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation parameter) instead of an ...
Satoru Odake, Ryu Sasaki
openalex +5 more sources
On linearly related sequences of difference derivatives of discrete orthogonal polynomials [PDF]
Journal of Computational and Applied Mathematics, 2014 R. Álvarez-Nodarse +3 more
openalex +3 more sources
New determinant expressions of multi-indexed orthogonal polynomials in discrete quantum mechanics [PDF]
, 2017 The multi-indexed orthogonal polynomials (the Meixner, little $q$-Jacobi (Laguerre), ($q$-)Racah, Wilson, Askey-Wilson types) satisfying second order difference equations were constructed in discrete quantum mechanics.
Satoru Odake
openalex +3 more sources
Some discrete multiple orthogonal polynomials
Journal of Computational and Applied Mathematics, 2003 27 pages, no figures.-- MSC2000 codes: 33C45, 33C10, 42C05, 41A28.-- Issue title: "Proceedings of the 6th International Symposium on Orthogonal Polynomials, Special Functions and their Applications" (OPSFA-VI, Rome, Italy, 18-22 June 2001). MR#: MR1985676 (2004g:33015) Zbl#: Zbl 1021.33006 In this paper, we extend the theory of discrete orthogonal ...
J. Arvesú +2 more
openalex +3 more sources
Symmetries for Casorati determinants of classical discrete orthogonal polynomials [PDF]
, 2013 Antonio J. Durán
openalex +2 more sources