The Fourier transform in Schwartz space - Peña Miranda, Carlos Alberto (2021)
The objective of this work is to study some properties and applications of the Schwartz space. Initially, the Fourier transform is used to demonstrate the transform of the derivative and derivative of the transform. Then the completeness of the Schwartz space is studied and some properties are demonstrated. Finally the Fourier inversion formula and Plancherel’s theorem are proved.