# Fourrier Tranform and schwartz space

1. Jan 30, 2012

### Stephen88

^_f=fourrier transform of f.
f_k=f<sub>k
sqrt= square root

The function f belongs to the schwartz space and k>0 f_k(x)=f(kx).
1)show that f_k also belongs to the schwartz space and ^_f(e)=(1/k)^_f(e/k)
2)the fourrier transform of exp((−x^2)/2) is sqrt(2pi)*exp((−e^2)/2) use the first part to obtain the fourrier transform for exp(−ax^2)

Attempt:
f belongs to the schwartz space then f is infinitly diff also f(kx)=kf(x) which belongs to the schwartz space.
then f_k(x)=f(kx)=kf(x) which belongs to the schwartz space.
I don't know if this is correct or how to continue...any help will be great.Thank you

2. Jan 30, 2012

### Stephen88

Should I change something ?