There are some functions which are invariant under Fourier transformation up to scaling factors, eg. sech(pi*x), Gaussian function etc.. Is there a set of basis functions, which form an invariant basis set? (eg like sine cosine functions, not being invariant though) If you think that such a basis cannot exist, explain why this is so, or even better add a proof.
2026-03-26 02:54:11.1774493651
Is there a Fourier invariant basis?
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