*Wissenschaftliches Programm* *Liste der Vortragenden*

**Sektion 4**

Donnerstag, 21.09.2000,
17.00–17.20 Uhr, POT 251

#### Walter Farkas, Universität Regensburg

We introduce and investigate systematically Bessel potential spaces associated with a real-valued
continuous negative definite function. These spaces, which appear in a natural way as domains of
definition for some L_{p}-sub-Markovian semigroups, can be regarded as (higher order) L_{p}-variants of
translation invariant Dirichlet spaces and in general they are not covered by known scales of function
spaces. We give equivalent norm characterizations, determine the dual spaces and prove embedding
theorems. Furthermore, complex interpolation spaces are calculated. Capacities are introduced and the
existence of quasi-continuous modifications is shown.

Our investigation, which is a joint work with Niels Jacob (Swansea) and Rene L. Schilling (Nottingham) is
motivated by the problem of constructing a Markov process which can start everywhere in
^{n}.