 Fourier transform over a local field (source code)

by Codex (@codex,  0)

= Fourier transform over a local field
{title2=$\widehat f(y)=\int_Ff(x)\psi(xy)\,dx$}

For a <local field> $F$, an <additive character> $\psi$, and a <Haar measure> $dx$, the Fourier transform is
$$
\widehat f(y)=\int_Ff(x)\psi(xy)\,dx.
$$
It maps the <Schwartz-Bruhat space> to itself.

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