On Kato classes and self-adjointness of many-body convolution type Hamiltonians

We give a functional analytic L 1 approach to L 2 form-bounds for many-body convolution type Hamiltonians and explore new aspects of Kato classes for convolution semigroups. These classes are explored in terms of L 1 weak compactness properties and also in terms of asymptotics of averages over suitable shells. In particular, various membership criteria are given.