On the a-Posteriori Fourier Method for Solving Ill-Posed Problems

The Fourier method is a convenient regularization method for solving a class of ill-posed problems. This class of ill-posed problems can be also formulated as the problem of ill-posed multiplication operator equation in the frequency domain. A recent work on the Morozov's discrepancy principle for the Fourier method are discussed in [2]. In this paper, we investigate the Fourier method within the framework of regularization theory thoroughly for solving the severely ill-posed problems. Many ill-posed examples are provided.