Numerical analytic continuation by a mollification method based on Hermite function expansion

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. Data are only given approximately on the real axis. A mollification method based on expanded Hermite functions has been introduced to deal with the ill-posedness of the problem. We have shown that the mollification parameter can be chosen by a discrepancy principle and a corresponding error estimate has also been obtained. Numerical tests are given to show the effectiveness of the method.