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- aggregation classification "A1".
- aggregation creator person.
- aggregation creator person.
- aggregation creator person.
- aggregation date "2011".
- aggregation format "application/pdf".
- aggregation hasFormat 2038186.bibtex.
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- aggregation isPartOf urn:issn:1069-5869.
- aggregation language "eng".
- aggregation rights "I have transferred the copyright for this publication to the publisher".
- aggregation subject "Mathematics and Statistics".
- aggregation title "The class of Clifford-Fourier transforms".
- aggregation abstract "Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical Fourier transform. This is applied to the so-called Clifford-Fourier transform (see Brackx et al., J. Fourier Anal. Appl. 11:669-681, 2005). The integral kernel of this transform is a particular solution of a system of PDEs in a Clifford algebra, but is, contrary to the classical Fourier transform, not the unique solution. Here we determine an entire class of solutions of this system of PDEs, under certain constraints. For each solution, series expressions in terms of Gegenbauer polynomials and Bessel functions are obtained. This allows to compute explicitly the eigenvalues of the associated integral transforms. In the even-dimensional case, this also yields the inverse transform for each of the solutions. Finally, several properties of the entire class of solutions are proven.".
- aggregation authorList BK440280.
- aggregation endPage "1231".
- aggregation issue "6".
- aggregation startPage "1198".
- aggregation volume "17".
- aggregation aggregates 2038187.
- aggregation aggregates 2064260.
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- aggregation similarTo s00041-011-9177-2.
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