Multidimensional sampling theorems for multivariate discrete transforms

Abstract This paper is devoted to the establishment of two-dimensional sampling theorems for discrete transforms, whose kernels arise from second order partial difference equations. We define a type operator and investigate its spectral properties. Green’s function constructed that generate orthonormal basis eigenvectors are defined. A Kramer-type lemma introduced two Lagrange interpolation proved. Several illustrative examples depicted. The theory extendible higher settings.