I'll write everything down from the start.
First, the notation:
Then the theorem:
If is summable for every , then
, where denotes Fourier transform of f.
Now, the problem.
We're supposed to prove this using induction on , and I just can't do it. The definition of is somewhat confusing, and I would b really grateful if someone could help me out, just for the basis, and I will try to work from there.