a mollification regularization method for stable analytic continuation

in this paper, we consider an analytic continuation problem on a strip domain with the data given approximately only on the real axis. the gauss mollification method is proposed to solve this problem. an a priori error estimate between the exact solution and its regularized approximation is obtained. moreover, we also propose a new a posteriori parameter choice rule and get a good error estimate. several numerical examples are provided, which show the method works effectively.