Results 1 to 10 of about 67,871 (69)

On discrete orthogonal polynomials of several variables [PDF]

, 2004
Let $V$ be a set of isolated points in $\RR^d$. Define a linear functional $\CL$ on the space of real polynomials restricted on $V$, $\CL f = \sum_{x \in V} f(x)\rho(x)$, where $\rho$ is a nonzero function on $V$.
Xu, Yuan
core   +4 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.
Gendenshtein L. E., Kurokawa N., Ryu Sasaki, Satoru Odake, Shintani T.   +4 more
core   +3 more sources

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

On zeros of discrete orthogonal polynomials [PDF]

, 2009
This article is available open access through the publisher’s website at the link below. Copyright @ 2008 Elsevier Inc.We exploit difference equations to establish sharp inequalities on the extreme zeros of the classical discrete orthogonal polynomials ...
Alexander Zarkh, Chihara, Ilia Krasikov, Ismail, Ismail, Krasikov, Krasikov, Krasikov, Krasikov, Krasikov, Levenshtein, Levenstein, Levit, Máté, Nikiforov, Szegö   +15 more
core   +1 more source

Variations of Stieltjes-Wigert and q-Laguerre polynomials and their recurrence coefficients

, 2014
We look at some extensions of the Stieltjes-Wigert weight functions. First we replace the variable x by x^2 in a family of weight functions given by Askey in 1989 and we show that the recurrence coefficients of the corresponding orthogonal polynomials ...
Boelen, Lies, Van Assche, Walter
core   +1 more source

A Probablistic Origin for a New Class of Bivariate Polynomials [PDF]

, 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 ...
Hoare, Michael R., Rahman, Mizan
core   +2 more sources

Quantum state transfer in spin chains with q-deformed interaction terms [PDF]

, 2010
We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest neighbour interaction strengths and the ...
Chakrabarti R, E I Jafarov, Golub G H, J Van der Jeugt, Kay A, Koekoek R Swarttouw R F, L'Innocente S, Regniers G   +7 more
core   +3 more sources

Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality

, 2012
A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the su(2) generators.
Alexei Zhedanov, Atakishiyev N M, Luc Vinet, Niederer U, Niederer U, Vincent X Genest, Vinet L, Wang X, Wigner E P   +8 more
core   +1 more source

Multi-indexed (q-)Racah Polynomials [PDF]

, 2012
As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials.
Andrews G E, Bannai E, Chakrabarti R, Darboux G, Fernández D J, Gendenshtein L E, Gladwell G M L, Grandati Y, Gómez-Ullate D, Ho C-L, Ho C-L, Ismail M E H, Koekoek R Swarttouw R F, Krein M G, Odake S, Odake S, Odake S, Parthasarathy P R, Quesne C, Quesne C, Quesne C, Ryu Sasaki, Sasaki R, Satoru Odake, Vinet L Zhedanov A   +24 more
core   +4 more sources

Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles [PDF]

, 2008
In [49] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials.
Borodin, Alexei, Strahov, Eugene
core   +3 more sources