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I was looking at a question on a physics forum (https://physics.stackexchange.com/questions/45955/splitting-light-into-colors-mathematical-expression-fourier-transforms) and I wanted a more mathematical perspective on it. How would such a convolution of a gaussian path integral as defined in arxiv.org/pdf/1110.2346 with a fourier transform be defined? Is such a thing even mathematically (or physically) meaningful? Please give me your opinions. Thanks in advance!

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    I think it would be best if you added a *precise* (or as precise as possible) statement of your question to it.2012-12-10

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