Fourier Transforms and Their Applications

This chapter deals with Fourier transforms in $$L^{1}(\mathbb{R})$$ and in $$L^{2}(\mathbb{R})$$ Space and their basic properties. Special attention is given to the convolution theorem and summability kernels including Cesáro, Fejér, and Gaussian kernels. Several important results including the approximate identity theorem, general Parseval’s relation, and Plancherel theorem are proved.