MPEJ Volume 14, No. 3, 21 pp.
Received: Sep 10, 2008. Accepted: Dec 20, 2008.


J. Kellendonk, S. Richard
On the structure of the wave operators in one dimensional potential scattering


ABSTRACT: In the framework of one dimensional potential scattering we prove
that, modulo a compact term, the wave operators can be written in terms of a
universal operator and of the scattering operator.  The universal operator is
related to the one dimensional Hilbert transform and can be expressed as a
function of the generator of dilations.  As a consequence, we show how
Levinson's theorem can be rewritten as an index theorem, and obtain the
asymptotic behaviour of the wave operators at high and low energy and at large
and small scale.

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