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• W1873579427 abstract "We prove a structure formula for the wave operators in R^3 and their adjoints for a scaling-invariant class of scalar potentials V, under the assumption that zero is neither an eigenvalue, nor a resonance for -Delta+V. The formula implies the boundedness of wave operators on L^p spaces, 1 leq p leq infty, on weighted L^p spaces, and on Sobolev spaces, as well as multilinear estimates for e^{itH} P_c. When V decreases rapidly at infinity, we obtain an asymptotic expansion of the wave operators. The first term of the expansion is of order ^{-4}, commutes with the Laplacian, and exists when V in ^{-3/2-epsilon} L^2. We also prove that the scattering operator S = W_-^* W_+ is an integrable combination of isometries. The proof is based on an abstract version of Wiener's theorem, applied in a new function space." @default.
• W1873579427 created "2016-06-24" @default.
• W1873579427 creator A5058437827 @default.
• W1873579427 date "2011-01-03" @default.
• W1873579427 modified "2023-09-27" @default.
• W1873579427 title "Structure of wave operators in R^3" @default.
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