Generalized Zernike or disc polynomials: an application in quantum optics

DOI10.1016/j.cam.2007.12.009zbMath1151.81049OpenAlexW1983395219MaRDI QIDQ955084

B. E. Eshmatov

Publication date: 18 November 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.12.009

zbMATH Keywords

Jacobi polynomials\(su(2)\) and \(su(1,1)\) Lie algebrastwo-mode interaction processes

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Quantum optics (81V80) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (12)

On the structure of polyharmonic Bergman-type spaces over the unit disk ⋮ Recursive computation of generalised Zernike polynomials ⋮ Computation of power law equilibrium measures on balls of arbitrary dimension ⋮ Polyharmonic Bergman spaces and Bargmann type transforms ⋮ Unitarily invariant strictly positive definite kernels on spheres ⋮ Differentiability of bizonal positive definite kernels on complex spheres ⋮ Zernike functions, rigged Hilbert spaces, and potential applications ⋮ Characterization of strict positive definiteness on products of complex spheres ⋮ Generalized Zernike polynomials: operational formulae and generating functions ⋮ k-holomorphic functions in spaces of several complex variables ⋮ The Hilbert-Schmidt norm of Hankel operators on poly-Bergman spaces ⋮ 2D-Zernike polynomials and coherent state quantization of the unit disc

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• Singular value decomposition for the 2D fan-beam Radon transform of tensor fields
• On Jacobi and continuous Hahn polynomials
• Four sets of₃F₂(1) functions, Hahn polynomials and recurrence relations for the 3-j coefficients

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