Hi! (Merry Christmas and happy holidays!! I hope you guys have a good time)

Exercise

Proof: (F, ||-||_H) is a Banach space, where

( fourier transform)

and

Definition

If the norm on F is complete (that is, any Cauchy sequence in F is convergent), then F is called a Banach space

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According to the Cauchy sequence/norm I'm at a loss what to do.

Thanks for all your time

Best regards,

Rapha.