- 04-422 Derezinski J., Fruboes R.
- Stationary van Hove limit
(56K, LATeX 2e)
Dec 22, 04
(auto. generated ps),
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Abstract. 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 E. B. Davies.
We compare both approaches.