Formula:619

Digital Library of Mathematical Functions ID 1.16.E41

${\displaystyle{\displaystyle\left\langle\mathscr{F}\left(1\right),\phi\right\rangle=\sqrt{2\pi}\left\langle\mathscr{F}\left(\mathscr{F}\left(\delta\right)\right),\phi\right\rangle=\sqrt{2\pi}\left\langle\mathscr{F}\left(\delta\right),\mathscr{F}(\phi)\right\rangle=\sqrt{2\pi}\left\langle\delta,\mathscr{F}(\mathscr{F}(\phi))\right\rangle=\sqrt{2\pi}\left\langle\delta,\phi_{-}\right\rangle=\sqrt{2\pi}\phi(0),}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\delta_{x}}}$:
• ${\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle}}$:
• ${\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}$: Fourier transform of a tempered distribution
• ${\displaystyle{\displaystyle\mathscr{F}(\phi)}}$: Fourier transform of a test function (locally)
• ${\displaystyle{\displaystyle\phi(x)}}$: test function
 

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