New method of bandlimited extrapolation

Abstract

The paper deals with numerical solution of the Fredholm integral equation associated with the classical problem of extrapolating bandlimited functions known on $(-1,1)$ to the entire real line. The approach presented can be characterized as the degenerate kernel method using the spherical Bessel functions as basis functions where the Tikhonov regularization is applied at the discrete level in order to deal with the ill-posedness of the problem.