Differential operator
Fourier interpretation

A differential operator P and its symbol appear naturally in connection with the Fourier transform as follows. Let ƒ be a Schwartz function. Then by the inverse Fourier transform,

This exhibits P as a Fourier multiplier. A more general class of functions p (x,ξ) which satisfy at most polynomial growth conditions in ξ under which this integral is well-behaved comprises the pseudo-differential operators.
keywords:existence, language:response_language[Dutch], punctuation:no_comma