The past and future wave operators on the singular spectrum

Details The past and future wave operators on the singular spectrum The past and future wave operators on the singular spectrum

2011-06-26

arxiv.org/abs/1106.5203v1

Mathematics

Functional Analysis

10 pages

Scientific paper

We consider averaged wave operators constructed for singular unitary operators $U_1$, $U_2$ and a bounded identification operator $A$. In the case of rank-two commutator $AU_1 - U_2A$, we show that averaged wave operators of past and future exist or do not exist simultaneously, and if they exist, they must coincide. As a consequence, we obtain some results concerning boundary behaviour of Cauchy-type integrals.

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