Multidimensional transform

Summary

A multidimensional transform is an integral transform, or a discrete analogue of one, applied to a function of several variables. The main examples are the multidimensional Fourier transform, the multidimensional Laplace transform, the multidimensional Mellin transform and, for sequences indexed by $\Z^n$, the multidimensional Z-transform. When the kernel is a product of one-variable kernels, the transform is the composition of one-variable transforms in each variable. Such transforms are used for partial differential equations, for images and other multidimensional signals, and in probability for joint distributions.