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by Ciro Santilli (@cirosantilli, 37)

The Fourier transform is a bijection in L2

 ... Integral Lebesgue integral Lebesgue integral of Lp is complete but Riemann isn't Lp space L2 Plancherel theorem
 0 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my 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
  2. L2
  3. Lp space
  4. Lebesgue integral of Lp is complete but Riemann isn't
  5. Lebesgue integral
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