Continuous fourier

1. May 27, 2014

Delta²

Can someone tell me if the continuous fourier transform of a continuous (and vanishing fast enough ) function is also a continuous function?

2. May 27, 2014

Xiuh

I can tell you more: in fact, if $f \in L^{1}(\mathbb R)$ then its Fourier Transform is uniformly continuous.

Last edited: May 27, 2014
3. May 28, 2014

Delta²

Thanks very much but can u ... remind me which functions belong to L1(R)?

4. May 28, 2014

micromass

Staff Emeritus
It are all the functions $f:\mathbb{R}\rightarrow \mathbb{R}$ which are absolutely integrable. That is, for which

$$\int_{-\infty}^{+\infty} |f(x)|dx$$

is finite (and the integral makes sense).

5. May 28, 2014

Thx again.