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Meixner-Pollaczek polynomials and the Heisenberg algebra
Tom H. Koornwinder
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TLDR
In this paper, an alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. 28, 509 (1987)].Abstract:
An alternative proof is given for the connection between a system of continuous Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev. Lett. 56, 2445 (1986); J. Math. Phys. 28, 509 (1987)]. The continuous Hahn polynomials turn out to be Meixner–Pollaczek polynomials. Use is made of the connection between Laguerre polynomials and Meixner–Pollaczek polynomials, the Rodrigues formula for Laguerre polynomials, an operational formula involving Meixner–Pollaczek polynomials, and the Schrodinger model for the irreducible unitary representations of the three‐dimensional Heisenberg group.read more
Citations
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Invariant differential operators on the Heisenberg group and Meixner–Pollaczek polynomials
Jacques Faraut,Masato Wakayama +1 more
TL;DR: In this paper, the authors extend this result in the framework of Gelfand pairs associated with the Heisenberg group and present a multivariable Meixner-Pollaczek polynomials.
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Orthogonal polynomials and operator orderings
Adel Hamdi,Jiang Zeng +1 more
TL;DR: In this paper, an alternative and combinatorial proof is given for a connection between a system of Hahn polynomials and identities for symmetric elements in the Heisenberg algebra, which was first observed by Bender, Mead, and Pinsky [Phys. Rev.
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Toeplitz Localization Operators: Spectral Functions Density
TL;DR: In this article, the authors consider two classes of localization operators based on Calderon and Gabor reproducing formulas and represent them in a uniform way as Toeplitz operators, and show that these spectral functions can be written in the form of a convolution of the generating symbol of TLO with a kernel function incorporating an admissible wavelet/window.
The Symmetric Meixner-Pollaczek polynomials
TL;DR: In this paper, the authors considered the problem of finding orthogonal polynomials on the real line with respect to any positive real measure for failing to satisfy Favard's three term recurrence relation condition.
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Generalized Meixner-Pollaczek polynomials
Stanisława Kanas,Anna Tatarczak +1 more
TL;DR: In this paper, the generalized Meixner-Pollaczek polynomials P λ (x; θ, ψ )o f a variable x ∈ R and parameters λ > 0,θ ∈ (0, π ), ψ ∈ r,d ef ined via the generating function
References
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Book
Groups and geometric analysis
TL;DR: Geometric Fourier analysis on spaces of constant curvature Integral geometry and Radon transforms Invariant differential operators Invariants and harmonic polynomials Spherical functions and spherical transforms Analysis on compact symmetric spaces Appendix Some details Bibliography Symbols frequently used Index Errata.
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations.
H.T. Koelink,J. Van der Jeugt +1 more
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The Hahn and Meixner polynomials of an imaginary argument and some of their applications
TL;DR: In this article, the Hahn and Meixner polynomials of a discrete variable are analytically continued in the complex plane both in variable and parameter, leading to the origination of two systems of real polynomial systems orthogonal with respect to a continuous measure.