 The ordinary continuous Fourier transform formula_387 is a TVS-automorphism of the Schwartz function space, and we will define the Fourier transform to be its transpose formula_388, which (abusing notation) will again be denoted by "F".So the Fourier transform of the tempered distribution "T" is defined by ("FT")("Ψ") = "T"("Fψ") for every Schwartz function "Ψ".