Taking this function on a member of a finite abelian group returns a member of the group that is the Pontryagin dual of the original group.
Taking this function on a member of a finite abelian group returns a member of the group that is the Pontryagin dual of the original group. The space of all functions whose derivatives are rapidly decreasing has the property that this operation is an automorphism; that space is named for Schwartz. The integral from negative infinity to infinity of the square of a function is equal to that same integral of this operation of that function, squared, according to Parseval's theorem. Like a related operation named for Laplace, it takes convolutions to products and takes inputs from the time domain to the frequency domain. For 10 points, name this operation which takes an input and resolves it into a series of frequencies, a transform named for a French mathematician.
Taking this function on a member of a finite abelian group returns a member of the group that is the Pontryagin dual of the original group.
Fourier transform