Clifford algebras, Fourier transforms, and quantum mechanics (Q4906059)

scientific article; zbMATH DE number 6137940

Language	Label	Description	Also known as
English	Clifford algebras, Fourier transforms, and quantum mechanics	scientific article; zbMATH DE number 6137940

Statements

instance of

scholarly article

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title

Clifford algebras, Fourier transforms, and quantum mechanics (English)

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author

Hendrik De Bie

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published in

Mathematical Methods in the Applied Sciences

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publication date

21 February 2013

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full work available at URL

https://arxiv.org/abs/1209.6434

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zbMATH Keywords

generalized Fourier transform

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fractional Fourier transform

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Dunkl transform

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radially deformed Fourier transform

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super Fourier transform

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Clifford analysis

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Clifford-Fourier transform

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Hermite semigroup

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MaRDI profile type

MaRDI publication profile

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Orthogonality of Hermite polynomials in superspace and Mehler type formulae

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The Fractional Order Fourier Transform and its Application to Quantum Mechanics

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Fractional convolution

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On a Hilbert space of analytic functions and an associated integral transform part I

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Immersion of the Fourier Transform in a Continuous Group of Functional Transformations

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Linear Canonical Transformations and Their Unitary Representations

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Canonical Transformations and Matrix Elements

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Canonical transforms. III. Configuration and phase descriptions of quantum systems possessing an s l (2,R) dynamical algebra

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Canonical transforms. I. Complex linear transforms

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Canonical transforms. II. Complex radial transforms

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Integral transforms in science and engineering

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Harmonic Analysis in Phase Space. (AM-122)

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Continuous vs. discrete fractional Fourier transforms

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Q3998721

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Differential-Difference Operators Associated to Reflection Groups

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Singular Polynomials for Finite Reflection Groups

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Generalized Hermite polynomials and the heat equation for Dunkl operators

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On the integrability of a representation of $\mathfrak{sl}(2,\mathbb R)$

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A positive radial product formula for the Dunkl kernel

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Wigner quantization of some one-dimensional Hamiltonians

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The $\mathfrak {su}(2)_\alpha $ Hahn oscillator and a discrete Fourier–Hahn transform

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Spectrum generating functions for non-canonical quantum oscillators

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Integral formulas for the minimal representation of $O(p,2$)

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THE INVERSION FORMULA AND HOLOMORPHIC EXTENSION OF THE MINIMAL REPRESENTATION OF THE CONFORMAL GROUP

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Spherical harmonics and integration in superspace

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Spherical harmonics and integration in superspace: II

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Q3043319

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Fourier transform and related integral transforms in superspace

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Hermite and Gegenbauer polynomials in superspace using Clifford analysis

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Hilbert space for quantum mechanics on superspace

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Orthosymplectically invariant functions in superspace

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Fundamental solutions for the super Laplace and Dirac operators and all their natural powers

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Schrödinger equation with delta potential in superspace

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Harmonic analysis on Heisenberg–Clifford Lie supergroups

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The Fourier transform on quantum Euclidean space

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Q5559954

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On the Clifford-Fourier Transform

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Special functions in Clifford analysis and axial symmetry

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Orthogonality of the generalized Hermitean Clifford–Hermite polynomials

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The Clifford-Fourier transform

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The two-dimensional Clifford-Fourier transform

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The Clifford-Fourier integral kernel in even dimensional Euclidean space

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The class of Clifford-Fourier transforms

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Dirac cohomology for graded affine Hecke algebras.

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Clifford analysis for finite reflection groups

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The Howe duality for the Dunkl version of the Dirac operator

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Dunkl operators and a family of realizations of $\mathfrak{osp}(1\vert2)$

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On the role of arbitrary order Bessel functions in higher dimensional Dirac type equations

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Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator

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The uncertainty principle: A mathematical survey

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An uncertainty principle for the Dunkl transform

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Q2743897

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Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra $\mathrm{Cl}_{3,0}$

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An uncertainty principle for quaternion Fourier transform

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Directional uncertainty principle for quaternion Fourier transform

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Clifford Fourier transform on multivector fields and uncertainty principles for dimensions $n=2\pmod 4$ and $n=3\pmod 4$

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Q5824493

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Convolution operator and maximal function for the Dunkl transform

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Hypercomplex Fourier and Laplace transforms. I

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Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case

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Hypercomplex Fourier Transforms of Color Images

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A general geometric Fourier transform convolution theorem

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The Paley-Wiener theorem in $\mathbb{R}^n$ with the Clifford analysis setting

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Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces

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Hypercomplex correlation techniques for vector images

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Identifiers

zbMATH Open document ID

1259.42001

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DOI

10.1002/mma.2679

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:4906059