Fourier analysis on space-like surfaces I. the case of mass ϰ ≠ 0

Abstract

Some spaces of functions or functionals on any space-like surface and those on the momentum space are considered. Fourier transformations are defined appropriately on these spaces, and it follows that these transformations are continuous and have their respective continuous inverses. Invariant singular functions are defined, and many physically important relations hold properly with respect to these singular functions.