The weak coupling (van Hove) limit of one parameter groups of contractions is studied by the stationary approach. We show that the resolvent of the properly renormalized and rescaled generator of a contractive semigroup has a limit as the coupling constant goes to zero. This limit is the resolvent of the generator of a certain contractive semigroup. Our results can be viewed as a stationary counterpart to the well known results about the weak coupling limit obtained by the time-dependent approach, due to Davies. We compare both approaches.
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