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Spectral distributions for long range perturbations. (English) Zbl 1088.35041

The author studies distributions (spectral distributions) that generalize the concept of spectral shift functions to the case of long-range perturbations of pseudodifferential operators. He proves relations between spectral distributions and relative scattering determinants and he defines a regularized scattering phase. The relations that he obtains are analogous to the ones for the standard spectral shift function. Furthermore, the high-energy and the semiclassical limits are studied. In particular, Breit-Wigner formulae are proven for long-range potentials.

MSC:

35P25 Scattering theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81U20 \(S\)-matrix theory, etc. in quantum theory
81U05 \(2\)-body potential quantum scattering theory
35S05 Pseudodifferential operators as generalizations of partial differential operators
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