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Operator Exponentials for the Clifford Fourier Transform on Multivector Fields in Detail

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Abstract

In this paper we study Clifford Fourier transforms (CFT) of multivector functions taking values in Clifford’s geometric algebra, hereby using techniques coming from Clifford analysis (the multivariate function theory for the Dirac operator). In these CFTs on multivector signals, the complex unit \({i \in \mathbb{C}}\) is replaced by a multivector square root of −1, which may be a pseudoscalar in the simplest case. For these integral transforms we derive an operator representation expressed as the Hamilton operator of a harmonic oscillator.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium

    David Eelbode

  2. Department of Material Science, College of Liberal Arts, International Christian University, Mitaka, Japan

    Eckhard Hitzer

Authors
  1. David Eelbode
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  2. Eckhard Hitzer
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Correspondence to David Eelbode.

Additional information

In memoriam of Prof. John Stephen Roy Chisholm, 5 November 1926 (Barnet, Hertfordshire, England) – 10 August 2015 (Kent, England) [22].

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Eelbode, D., Hitzer, E. Operator Exponentials for the Clifford Fourier Transform on Multivector Fields in Detail. Adv. Appl. Clifford Algebras 26, 953–968 (2016). https://doi.org/10.1007/s00006-015-0600-7

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  • DOI: https://doi.org/10.1007/s00006-015-0600-7

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