The Clifford-Fourier Transform

The Clifford-Fourier Transform

A pair of Clifford-Fourier transforms is defined in the framework of Clifford analysis, as operator exponentials with a Clifford algebra-valued kernel. It is a genuine Clifford analysis construct, which is shown to be a refinement of the classical multi-dimensional Fourier transform. An adequate ope...

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Veröffentlicht in:The Journal of fourier analysis and applications 2005-12, Vol.11 (6), p.669-681
Hauptverfasser: Brackx, Fred, De Schepper, Nele, Sommen, Frank
Format: Artikel
Sprache:eng
Schlagworte:
Fourier analysis
Fourier transforms
Mathematical analysis
Operational calculus
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Zusammenfassung:A pair of Clifford-Fourier transforms is defined in the framework of Clifford analysis, as operator exponentials with a Clifford algebra-valued kernel. It is a genuine Clifford analysis construct, which is shown to be a refinement of the classical multi-dimensional Fourier transform. An adequate operational calculus is developed.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-005-4079-9