ISSN:
1432-0916
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
,
Physik
Notizen:
Abstract We consider scattering for the equation (□+m 2)ϕ+λϕ3=0 on four-dimensional Minkowski space. Form〉0, one-to-one and onto wave operatorsW ± λ :H→H are known to exist for all λ≧0, whereH denotes the Hilbert space of finite-energy Cauchy data. We prove that the maps (λ,u)↦W ± λ (u) and (λ,u)↦(W ± λ )−1 (u) are continuous from [0, ∞)×H toH, and extend to real-analytic functions from an open neighborhood of {0}×H∪ℝ×{0}⊂ℝ×H to the Hilbert spaceH −1 of Cauchy data with Poincaré-invariant norm. Form=0, wave operatorsW ± λ are known to exist as diffeomorphisms ofH for all λ≧0, where hereH denotes the Hilbert space of finite Einstein energy Cauchy data. In this case we prove that the maps (λ,u)↦(W ± λ ) (u) and (λ,u)↦(W ± λ )−1 (u) extend to real-analytic functions from a neighborhood of [0, ∞)×H⊂ℝ×H toH.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1007/BF01218466
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