Gamow state vectors as functionals over subspaces of the nuclear space

Exponentially decaying Gamow state vectors are obtained from S-matrix poles in the lower half of the second sheet, and are defined as functionals over a subspace of the nuclear space, PHI. Exponentially growing Gamow state vectors are obtained from S-matrix poles in the upper half of the second sheet, and are defined as functionals over another subspace of PHI. On functionals over these two subspaces the dynamical group of time development splits into two semigroups