= Plancherel theorem
{c}
Some sources say that this is just the part that says that the <norm (mathematics)> of a <l2> function is the same as the norm of its <Fourier transform>.
Others say that this theorem actually says that the <Fourier transform> is <bijective>.
The comment at https://math.stackexchange.com/questions/446870/bijectiveness-injectiveness-and-surjectiveness-of-fourier-transformation-define/1235725\#1235725 may be of interest, it says that the <bijection> statement is an easy consequence from the <norm (mathematics)> one, thus the confusion.
TODO does it require it to be in <l1 space> as well? <Wikipedia> https://en.wikipedia.org/w/index.php?title=Plancherel_theorem&oldid=987110841 says yes, but https://courses.maths.ox.ac.uk/node/view_material/53981 does not mention it.