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**^_f=fourrier transform of f.**

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