Coherent states and Hermite polynomials on quaternionic Hilbert spaces

DOI10.1088/1751-8113/43/38/385205zbMath1198.81126OpenAlexW2094867207MaRDI QIDQ3161097

Adam Krzyżak, G. Honnouvo, K. Thirulogasanthar

Publication date: 11 October 2010

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8113/43/38/385205

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Coherent states (81R30)

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Multivariate holomorphic Hermite polynomials ⋮ Kibble-Slepian formula and generating functions for 2D polynomials ⋮ Coherent states on quaternion slices and a measurable field of Hilbert spaces ⋮ On the dimensions of oscillator algebras induced by orthogonal polynomials ⋮ A review of multivariate orthogonal polynomials ⋮ A representation of Weyl-Heisenberg Lie algebra in the quaternionic setting ⋮ Coherent state quantization of quaternions ⋮ On some 2𝐷 orthogonal 𝑞-polynomials ⋮ General construction of reproducing kernels on a quaternionic Hilbert space ⋮ Two variable extensions of the Laguerre and disc polynomials ⋮ Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states ⋮ S-spectrum and associated continuous frames on quaternionic Hilbert spaces ⋮ Complex Hermite polynomials: Their combinatorics and integral operators ⋮ Discrete frames on finite dimensional left quaternion Hilbert spaces ⋮ Spectral analysis on planar mixed automorphic forms ⋮ Analytic properties of complex Hermite polynomials ⋮ Canonical, Squeezed and Fermionic Coherent States in a Right Quaternionic Hilbert Space with a Left Multiplication on It ⋮ Generalized 2D Laguerre polynomials and their quaternionic extensions ⋮ Squeezed states in the quaternionic setting ⋮ Classes of bivariate orthogonal polynomials

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