Research proof index

The compact normalized $L^p$ norm is unchanged by conjugating a function and reflecting its argument: $\|x\mapsto\overline{f(-x)}\|_p=\|f\|_p$.

Hölder's inequality, binary case.

Translation preserves the compact normalized $L^p$ norm: for every group element $a$, $\|\tau_a f\|_{p}=\|f\|_{p}$.

Hölder's inequality, binary case.

Parseval-Plancherel identity for the discrete Fourier transform.