Abstract:
We use the well-studied Friedrichs model to showcase a new method for proving the asymptotic completeness of two operators, which in our case are the Friedrichs operator $A$ and the operator obtained from $A$ by omitting the integral term. Technically, the problem is reduced to a detailed analysis of the Fredholm determinant and minor of an auxiliary integral operator.
Key words and phrases:asymptotic completeness, Friedrichs model, wave operators, Fredholm minor, Fredholm determinant, stationary phase method.
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