A convergence theorem on a kind of band-limited functions with applications

A theorem on the convergence of a particular sequence of bandlimited functions is proved. As its applications, the convergence of a speed up error energy reduction algorithm for extrapolating bandlimited functions in noiseless cases and the convergence of an iterative algorithm to obtain estimations of bandlimited functions in noise cases are derived. Both algorithms are the improved versions of the Papoulis-Gercheberg algorithm.Institute of Systems Science, Academia Sinica