Spectral and scattering theory for symbolic potentials of order zero

Details Spectral and scattering theory for symbolic potentials of order zero Spectral and scattering theory for symbolic potentials of order zero

2001-12-17

arxiv.org/abs/math/0112163v1

Mathematics

Analysis of PDEs

69 pages

Scientific paper

The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on the Euclidean plane which are homogeneous of degree zero near infinity. The most complete results require the additional assumption that the restriction of the potential to the circle(s) at infinity be Morse. Generalized eigenfunctions associated to the essential spectrum at non-critical energies are shown to originate both at minima and maxima, although the latter are not germane to the $L^2$ spectral theory. Asymptotic completeness is shown, both in the traditional $L^2$ sense and in the sense of tempered distributions. This leads to a definition of the scattering matrix, the structure of which will be described in a future publication.

Affiliated with

Also associated with

No associations

Rating

Spectral and scattering theory for symbolic potentials of order zero does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral and scattering theory for symbolic potentials of order zero, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral and scattering theory for symbolic potentials of order zero will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-261695