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A general geometric Fourier transform convolution theorem. (English) Zbl 1263.15021
Summary: The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of “A general geometric Fourier transform” by the authors [Proceedings of the 9th international conference on Clifford algebras and their applications, Bauhaus-University Weimar, Germany (2011)], covering most versions in the literature. We show which constraints are additionally necessary to obtain certain features like linearity, a scaling, or a shift theorem. In this paper, we extend the former results by a convolution theorem.
MSC:
15A66Clifford algebras, spinors
43A32Other transforms and operators of Fourier type
44A35Convolution (integral transforms)
References:
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