The Fractional Clifford-Fourier Kernel

Craddock, MJ; Hogan, JA

The Fractional Clifford-Fourier Kernel

Craddock, MJ Hogan, JA

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Publication Type:: Journal Article
Citation:: Journal of Fourier Analysis and Applications, 2013, 19 (4), pp. 683 - 711
Issue Date:: 2013-08-01

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Field	Value	Language
dc.contributor.author	Craddock, MJ	en_US
dc.contributor.author	Hogan, JA	en_US
dc.date.issued	2013-08-01	en_US
dc.identifier.citation	Journal of Fourier Analysis and Applications, 2013, 19 (4), pp. 683 - 711	en_US
dc.identifier.issn	1069-5869	en_US
dc.identifier.uri	http://hdl.handle.net/10453/27092
dc.description.abstract	The Clifford-Fourier transform was introduced by Brackx, De Schepper and Sommen who subsequently computed its kernel in dimension d=2. Here we compute the kernel of a fractional version of the transform when d=2 and 4. In doing so we solve appropriate wave-type problems on spheres in two and four dimensions. We also give formulae for the solutions of these problems in all even dimensions and hence a means of computing the fractional Clifford-Fourier kernels in even dimensions. © 2013 Springer Science+Business Media New York.	en_US
dc.relation.ispartof	Journal of Fourier Analysis and Applications	en_US
dc.relation.isbasedon	10.1007/s00041-013-9274-5	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	The Fractional Clifford-Fourier Kernel	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	19	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	19	en_US

Abstract:

The Clifford-Fourier transform was introduced by Brackx, De Schepper and Sommen who subsequently computed its kernel in dimension d=2. Here we compute the kernel of a fractional version of the transform when d=2 and 4. In doing so we solve appropriate wave-type problems on spheres in two and four dimensions. We also give formulae for the solutions of these problems in all even dimensions and hence a means of computing the fractional Clifford-Fourier kernels in even dimensions. © 2013 Springer Science+Business Media New York.

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http://hdl.handle.net/10453/27092