A wavelet regularization method for solving numerical analytic continuation

In this paper we consider the problem of analytic continuation of analytic function on a strip domain, where the data are given only on the real axis. This is an ill-posed problem. The occurrence of its ill-posedness is intrinsically due to the high-frequency perturbation of data. However, Meyer wavelet has compact support in the frequency space. By expanding the data and the solution in a basis of Meyer wavelets, high-frequency components can be filtered away, and the Hölder-type stability estimates for both a priori and a posteriori choice rules are obtained. Numerical illustrations show that the method works effectively.