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arXiv · 1106.5203

The past and future wave operators on the singular spectrum

R. V. Bessonov
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Abstract

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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R. V. Bessonov. 2011-06-26. The past and future wave operators on the singular spectrum. https://arxiv.org/abs/1106.5203

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