Integral transforms, convolution products, and first variations.
Kim, Bong Jin, Kim, Byoung Soo, Skoug, David (2004)
International Journal of Mathematics and Mathematical Sciences
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Kim, Bong Jin, Kim, Byoung Soo, Skoug, David (2004)
International Journal of Mathematics and Mathematical Sciences
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The aim of this paper is to show that, in various situations, the only continuous linear (or not) map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups ℤ/nℤ, the integers ℤ, the torus 𝕋 and the real line. We also ask a related question for the twisted convolution.
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Kim, Jeong Gyoo, Ko, Jung Won, Park, Chull, Skoug, David (1999)
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Stevan Pilipović (1988)
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Nedeljkov, M., Pilipović, S. (1992)
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Baccar, C., Hamadi, N.B., Rachdi, L.T. (2006)
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E. Gesztelyi (1970)
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Computerized tomograhphy is a technique for computation and visualization of density (i.e. X- or -ray absorption coefficients) distribution over a cross-sectional anatomic plane from a set of projections. Three-dimensional reconstruction may be obtained by using a system of parallel planes. For the reconstruction of the transverse section it is necessary to choose an appropriate method taking into account the geometry of the data collection, the noise in projection data, the amount...