 Let
formula_400 be a rapidly decreasing tempered distribution or, equivalently,
formula_401 be an ordinary (slowly growing, smooth) function within the space of tempered distributions and let
formula_402 be the normalized (unitary, ordinary frequency) Fourier transform 

then, according to ,

hold within the space of tempered distributions


.In particular, these equations become the Poisson Summation Formula
if formula_405 is the Dirac Comb
.The space of all rapidly decreasing tempered distributions is also called the space of "convolution operators" formula_406 and
the space of all ordinary functions within the space of tempered distributions is also 
called the space of "multiplication operators" formula_407.