Two Dimensional Fourier-Laplace Transforms and Testing Function Spaces

In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions. One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation to a frequency domain representation. The two dimensional Laplace transformation is useful in the solution of non-homogeneous partial differential equations.

The proposed paper provides the generalization of two dimensional Fourier-Laplace transform in the distributional sense. Different types of testing function spaces by using Gelfand-Shilov technique and some topological properties are defined.