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In Fourier analysis, we can decompose a function into sine waves with different wavenumbers that travel at different speeds (i.e., for a given wavenumberkthey can have different frequencies ω and therefore different speedsv= ω/k). There is no upper bound on the speed of propagationvfor an ordinary Fourier transform. I am wondering whether it is possible to similarly represent a function in Minkowski space by a superposition of some convenient functions (e.g., we could still use sine waves if we only have 1 spatial and 1 temporal dimension) that propagate at speeds LESS thanc.

The specific application I have in mind is to represent an arbitrary charge distribution as a superposition of charge distributions moving inertially (ideally, at speeds less thanc).

Thanks for your help.

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# Fourier transform in Minkowski space

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