Sampling type reconstruction processes for the disk algebra

This paper considers the classical problem of recovering functions in the disk algebra from discrete samples taken at the unit circle by means of linear sampling type approximation methods. The paper characterizes subspaces of the disk algebra on which linear approximation operators do exist and subspaces on which such operators do not exist. The subspaces on which a linear signal recovery is possible are characterized by a sufficient concentration of the signal energy in the low frequency components of the signal.