Formula:612

Digital Library of Mathematical Functions ID 1.16.E36

${\displaystyle{\displaystyle\left\langle\mathscr{F}\left(P(\mathbf{D})u\right),\phi\right\rangle=\left\langle P_{-}\mathscr{F}\left(u\right),\phi\right\rangle=\left\langle\mathscr{F}\left(u\right),P_{-}\phi\right\rangle,}}$

Symbols List

• ${\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle}}$:
• ${\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}$: Fourier transform of a tempered distribution
• ${\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}$: test function
• ${\displaystyle{\displaystyle\mathbf{D}}}$: vector differential operator (locally)
• ${\displaystyle{\displaystyle P}}$: polynomial of several variables
• ${\displaystyle{\displaystyle Df}}$:
 

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