Research proof index

For a complex-valued function on the ambient finite group and a nonzero even integer $n$, ordinary self-convolution has no larger normalized $L^n$ norm than self-difference-convolution: $\|f*f\|_n\le\|f\mathbin{\circleddash}f\|_n$.

For a complex-valued function and a nonzero even integer $n$, discrete self-convolution has no larger $L^n$ norm than discrete self-difference-convolution: $\|f*f\|_n\le\|f\mathbin{\circleddash}f\|_n$.