On asymptotic equipartition of energy

AbstractA particular class of selfadjoint 2 × 2 operator matrices A of the form A = (0BB∗0) acting on a direct sum Hilbert space H = H1 ⊕ H2, Hi, i = 1, 2, Hilbert spaces, is considered. The square of the norm (i.e., the energy) of a solution of the corresponding initial value problem is shown to be distributed asymptotically evenly to its first and second component as t → ±∞ if the initial values are in the absolute continuous subspace. The result extends and simplifies proofs of results obtained previously in this area. A list of examples covered by the general results is included