  The Anderson localization problem in one and two dimensions is solved
analytically via the calculation of the generalized Lyapunov exponents. This is
achieved by making use of signal theory. The phase diagram can be analyzed in
this way. In the one dimensional case all states are localized for arbitrarily
small disorder in agreement with existing theories. In the two dimensional case
for larger energies and large disorder all states are localized but for certain
energies and small disorder extended and localized states coexist. The phase of
delocalized states is marginally stable. We demonstrate that the
metal-insulator transition should be interpreted as a first-order phase
transition. Consequences for perturbation approaches, the problem of
self-averaging quantities and numerical scaling are discussed.
