Plancherel's theorem is a fundamental result in harmonic analysis that establishes the equivalence of the Fourier transform and the L2 norm of a function. This theorem asserts that the Fourier transform preserves the inner product structure of functions in the L2 space, meaning that the energy of a signal is conserved under transformation. It connects deeply with various properties of Fourier transforms, making it crucial for understanding inversion formulas and Parseval's identity.
congrats on reading the definition of Plancherel's theorem. now let's actually learn it.