 Because the Fourier transform changes differentiation by "x""α" into multiplication by "x""α" and vice versa, this symmetry implies that the Fourier transform of a Schwartz function is also a Schwartz function.A sequence formula_367 of functions in "S"(R"n") converges to 0 in "S"(R"n") if and only if the functions formula_368 converge to 0 "uniformly" in the whole of formula_85, which implies that such a sequence must converge to zero in formula_370.The space of test functions formula_371 is dense in "S"(R"n") are is the set of all analytic functions that belong to "S"(R"n").