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Symbolic functional calculus and \(N\)-body resolvent estimates. (English) Zbl 0960.58025

The authors construct a functional calculus for symbolic functions of scattering pseudo-differential operators on manifolds with boundaries. As an application they construct the plane waves for an \(N\)-body short range Schrödinger operator and obtain an estimate for the scattering wavefront.

MSC:

58J99 Partial differential equations on manifolds; differential operators
58J40 Pseudodifferential and Fourier integral operators on manifolds
35P25 Scattering theory for PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
47A60 Functional calculus for linear operators
81U10 \(n\)-body potential quantum scattering theory
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References:

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