Some extensions of Paley-Wiener theorem (Q1266288)

The authors extend the Shannon sampling theorem for Paley-Wiener spaces in the plane to certain irregular sampling sequences that need not have the usual product form but can be taken in a two-dimensional neighborhood of the lattice points. Other conditions involving frames lead to more general irregular sampling theorems in the plane. The Shannon theorem is further extended from Paley-Wiener spaces to other wavelet subspaces in the plane. Both regular and irregular sampling theorems are proved for this case.