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• W3102635765 abstract "In this review, we give an overview of several recent generalizations of the Fourier transform, related to either the Lie algebra or the Lie superalgebra . In the former case, one obtains scalar generalizations of the Fourier transform, including the fractional Fourier transform, the Dunkl transform, the radially deformed Fourier transform, and the super Fourier transform. In the latter case, one has to use the framework of Clifford analysis and arrives at the Clifford–Fourier transform and the radially deformed hypercomplex Fourier transform.A detailed exposition of all these transforms is given, with emphasis on aspects such as eigenfunctions and spectrum of the transform, characterization of the integral kernel, and connection with various special functions. Copyright © 2012 John Wiley & Sons, Ltd." @default.
• W3102635765 created "2020-11-23" @default.
• W3102635765 creator A5004905591 @default.
• W3102635765 date "2012-09-18" @default.
• W3102635765 modified "2023-09-30" @default.
• W3102635765 title "Clifford algebras, Fourier transforms, and quantum mechanics" @default.
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• W3102635765 doi "https://doi.org/10.1002/mma.2679" @default.
• W3102635765 hasPublicationYear "2012" @default.
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