The fourier transform and its application in solving the equation

Abstract

Fourier transform is a linear transform that applicants in the field of engineering and physics. In this research study, we summarize the fundamental properties of the Fourier transform and its application in solving the wave equation. First, we review the definition of Fourier transform and its inverse form. Then, we show Schwartz space is the invariant subspace of the Fourier transform. We also prove the Plancherel theorem. At last, we apply the Fourier transform to solve the wave equation.