The Clifford-Fourier Transform Fo and Monogenic Extensions

Arnoldo Bezanilla Lopez; Omar Sanchez

doi:10.1007/s00006-010-0275-z

The Clifford-Fourier Transform Fo and Monogenic Extensions

Arnoldo Bezanilla Lopez, Omar Sanchez

Benemerita Universidad Autonoma de Puebla

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Abstract

In the last decade several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus, and a connection between the Fourier transform and this new transform. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.

Original language	English
Pages (from-to)	757-772
Journal	Advances in Applied Clifford Algebras
Volume	21
Issue number	4
Early online date	24 Oct 2010
DOIs	https://doi.org/10.1007/s00006-010-0275-z
Publication status	Published - Dec 2011

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10.1007/s00006-010-0275-z

1405.6398v1

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title = "The Clifford-Fourier Transform Fo and Monogenic Extensions",

abstract = "In the last decade several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus, and a connection between the Fourier transform and this new transform. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.",

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AB - In the last decade several versions of the Fourier transform have been formulated in the framework of Clifford algebra. We present a (Clifford-Fourier) transform, constructed using the geometric properties of Clifford algebra. We show the corresponding results of operational calculus, and a connection between the Fourier transform and this new transform. We obtain a technique to construct monogenic extensions of a certain type of continuous functions, and versions of the Paley-Wiener theorems are formulated.

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JO - Advances in Applied Clifford Algebras

JF - Advances in Applied Clifford Algebras

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The Clifford-Fourier Transform Fo and Monogenic Extensions

Abstract

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