Orthogonal polynomials and generalized oscillator algebras

DOI10.1080/10652460108819339zbMath1026.33007arXivmath/0002226OpenAlexW2031539232MaRDI QIDQ4409747

Vadim V. Borzov

Publication date: 30 June 2003

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0002226

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (21)

Orthogonal polynomials and deformed oscillators ⋮ Realization by a differential operator of the annihilation operator for generalized Chebyshev oscillator ⋮ On the dimensions of oscillator algebras induced by orthogonal polynomials ⋮ The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator ⋮ A class of vector coherent states defined over matrix domains ⋮ Local perturbation of the discrete Schrödinger operator and a generalized Chebyshev oscillator ⋮ \(N\)-symmetric Chebyshev polynomials in a composite model of a generalized oscillator ⋮ Calculation of the Mandel parameter for an oscillator-like system generated by generalized Chebyshev polynomials ⋮ Reproducing kernels and coherent states on Julia sets ⋮ A generating function and formulae defining the first-associated Meixner–Pollaczek polynomials ⋮ Chebyshev-Koornwinder oscillator ⋮ Compound model of the generalized oscillator. I ⋮ Generalized oscillator and its coherent states ⋮ On the dimensions of oscillator-like algebras induced by orthogonal polynomials: nonsymmetric case ⋮ Invariance of the generalized oscillator under a linear transformation of the related system of orthogonal polynomials ⋮ Generalized coherent states: a novel approach ⋮ Generalized coherent states for oscillators associated with the Charlier \(q\) -polynomials ⋮ Noncommutative reading of the complex plane through Delone sequences ⋮ Quaternionic vector coherent states and the supersymmetric harmonic oscillator ⋮ Generalized coherent states for \(q\)-oscillator associated with discrete \(q\)-Hermite polynomials ⋮ Research Article Orthogonal polynomials attached to coherent states for the symmetric Pöschl–Teller oscillator

Cites Work

• Unnamed Item
• Unnamed Item
• \(q\)-orthogonal polynomials and the oscillator quantum group
• On a general \(q\)-Fourier transformation with nonsymmetric kernels
• Notes on Generating Functions of Polynomials: (3) Polynomials of Legendre and Gegenbauer
• Notes on Generating Functions of Polynomials: (4) Jacobi Polynomials
• Notes on Generating Functions of Polynomials: (1) Laguerre Polynomials

This page was built for publication: Orthogonal polynomials and generalized oscillator algebras