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The Fourier transform is a bijection in L2

Ciro Santilli (@cirosantilli, 37) ... Integral Lebesgue integral Lebesgue integral of Lp is complete but Riemann isn't Lp space L2 Plancherel theorem
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own version
As mentioned at Section "Plancherel theorem", some people call this part of Plancherel theorem, while others say it is just a corollary.
This is an important fact in quantum mechanics, since it is because of this that it makes sense to talk about position and momentum space as two dual representations of the wave function that contain the exact same amount of information.

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  1. Plancherel theorem
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  4. Lebesgue integral of Lp is complete but Riemann isn't
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