Is there any theoretical or empirical research about planetary systems with a black hole in their center? I assume such a system would be hard to detect due to a lack of radiation, at least if the vicinity of the black hole does not contain a lot of mass which falls into it over time, thus creating (a lot of) radiation.

Since black hole formation in a supernova explosion is a process which destroys any planetary system around its original star, any planetary system around a black hole must have formed after black hole formation.

A few objections come to mind off-the-cuff: Because black holes have a large mass there is a minimum distance for planetary orbits below which they would disintegrate due to tidal forces. This may interfere with the usual evolution of planets (they clear their orbits and kick out interfering bodies, for example), because their "orbital space volume" becomes too large for them to keep clean, and the orbital period becomes long.

Is anything known or is there any speculation about such systems?
Since planets are known to exist around neutron stars (e.g. see Wolcznan &amp; Frail (1992); and see the list of "pulsar planets" - technically, these were the first exoplanets ever discovered), then it is difficult to see any fundamental reason why there should not be examples orbiting black holes. 

In fact, since it is probably feasible to form black holes via direct collapse, without an associated supernova then maybe the hazards for planets are not so severe.

Against this, must be set the fact that black hole progenitors are likely to be more massive than neutron star progenitors and the role of winds and radiation on the formation of planets is still not well established.

Planets orbiting neutron stars are/were found from a timing analysis of pulsar signals. The same phenomenenon is not present for black holes and direct imaging or observing a transit is not remotely feasible at present.