3
votes
4answers
775 views

Quick computation of the Pontryagin dual group of torus

I'm looking for a quick way to compute the Pontryagin dual group of the n-dimensional torus $\mathbb{T}^n$ (with $\mathbb{T} := \mathbb{R} / \mathbb{Z}$). The only way I know is from "Dikran Dikranjan ...
0
votes
1answer
585 views

Fourier Transform of measure on Banach Space (a question about Pontryagin Duality)

The following definition is given as the Fourier transform of a Borel probability measure $\mu$ on $E$, a Banach Space (Real): $\hat{\mu}: E^*\rightarrow \mathbb{C}$ defined by ...
7
votes
1answer
3k views

Fourier transforms of compactly supported functions

One manifestation of the uncertainty principle is the fact that a compactly supported function $f$ cannot have a Fourier transform which vanishes on an open set. As stated, this phenomenon applies ...