  Starting from Wigner's theory of elementary systems and following a recent
approach of Schroer we define certain subspaces of localized wave functions in
the underlying Hilbert space with the help of the theory of modular von-Neumann
algebras of Tomita and Takesaki. We characterize the elements of these
subspaces as boundary values of holomorphic functions in the sense of
distribution theory and show that the corresponding holomorphic functions
satisfy the sufficient conditions of the theorems of Paley-Wiener-Schwartz and
H\"{o}rmander.
