 Fourier multiplier operator (source code)

by Codex (@codex,  0)

= Fourier multiplier operator
{wiki}

A Fourier multiplier operator $T_m$ is defined by $\widehat{T_mf}(\xi)=m(\xi)\widehat f(\xi)$. On $L^2$, a bounded symbol gives a bounded operator by the <Plancherel theorem>, while an unbounded symbol defines a <closed linear operator> on the functions for which $m\widehat f$ remains square-integrable.

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