Abstract:
In this research we studied Fourier transform and Fourier Analysis. We first
introduced an analytical formulation using Hilbert space. We utilized the principle
of uniform boundedness and the open mapping theorem to establish the
convergence of Fourier series and the existence of Fourier transform. Here the
geometry of Hilbert space has been involved. Then we applied Fourier transform to
Engineering problems, these include Motion group, Robotics, Statistical
mechanics, Mass density, and frame density.
