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Generalized limiting absorption method and multidimensional inverse scattering theory
Author(s) -
Weder Ricardo
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140705
Subject(s) - limiting , mathematics , generalization , eigenvalues and eigenvectors , inverse scattering problem , inverse , scattering , scattering theory , mathematical analysis , quantum inverse scattering method , absorption (acoustics) , inverse problem , inverse scattering transform , physics , quantum mechanics , geometry , mechanical engineering , acoustics , engineering
We generalize the classical limiting absorption method. This generalization is applied to the study of the Faddeev–Lippmann–Schwinger equations in the Faddeev–Newton approach to multidimensional inverse scattering theory. In particular, we give a new proof, under more general conditions than were known previously, of the absence of exceptional points for small potentials and large values of the parameters, and on the existence of real exceptional points if there are complex ones, in particular for potentials that produce negative eigenvalues.