Complete analysis of the Eigen functions of Fourier transform

In this paper, we proposed an analysis of Eigen functions of the n-Dimensional Fourier transform. We extended the theory developed in our previous publication [1]. We applied our extended theory of systematic construction of Eigen function concept for sine and cosine functions. We explained the concept in a clear way through example construction of Eigen functions of 1-D and 2-D Fourier transform for real even case with negative Eigen value. PP Vaidyanathan discussed in his paper [2] that construction of complex Eigen function f₁+ jf₂ is possible when both functions f₁ and f₂ are either real even or real odd. But he didn´t discuss what will happen when f₁ and f₂ are different. We subjected this concept and derived the necessary expressions for complex Eigen functions when function f₁ is even and function f₂ is odd vice versa.