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I was looking at a question on a physics forum (http://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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You should try to provide more information in your question, instead of just posting links. Questions and answers on stackexchange are supposed to be helpful for other people as well as you, and should be somewhat self-contained. Not to mention that having to read a thread on another forum and a paper to just understand the question will deter most people from trying to help you. –  tomasz Dec 9 '12 at 3:22
    
Thanks for the feedback. Would MO be better for this question? How about if I copy-pasted the question from physics stackexchange and simply added more info on mathematical motivation, would that be sufficient or would it get deleted for being a duplicate? –  Roberty Psiy Dec 9 '12 at 19:21
    
I think it would be best if you added a precise (or as precise as possible) statement of your question to it. –  tomasz Dec 10 '12 at 4:02
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