Eigenfunction Expansions Associated with the Laplacian for Certain Domains with Infinite Boundaries. II. Applications to Scattering Theory
Charles Irwin Goldstein · Transactions of the American Mathematical Society · 1969
Januaryfor the solutions p°(x, t) of the wave equation in S with finite energy, which vanish on S. It is shown that f [\Vp°(x, t)\2+\p?(x,t)\2]dx-+0 asi-^±oo for each bounded subset B of S. No information is given, however, concerning the rate of decay.Finally, in §6 we extend the arguments of §4 to establish the existence, unitarity, and invariance of the wave operators W±(y(A112), (2)W|2]^.Jn