Fourier Transform of a Polytope and its Applications in Geometric Combinatorics

Fourier transform is a principal analysis tool which has been found to be especially useful for problem simplification in many fields of scientific endeavor. This paper is aimed to find the Fourier transform of the indictor function for a real closed polytope P of dimension d where it is proved in a main theorem. Some applications of Fourier transform are presented to show it's important.