I am a physicist, so forgive my ignorance... I would like to know if FT mapping is always unique in a sense discussed here. Correct me if I am wrong, but it looks like FT is uniques up to a phase and maybe a constant factor, correct? I would really appreciate if you share the info on the cases when FT is NOT unique, references etc.

Thanks in advance!

  • 1
    $\begingroup$ Different function with different phases can produce different Fourier transforms. To see that consider two different functions with magnitudes equal to 1 everywhere but with different phases. If two functions have the same L2 norm, then their Fourier transform is the same. So if two function differ only on a set i of measure 0, and their integral elements in a L2 sense, then their Fourier transforms are the same. $\endgroup$
    – NicNic8
    Jul 7, 2021 at 15:28


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