Zentrale Distributionen auf nilpotenten Liegruppen

We contribute some results to the following question discussed in several papers (3], 9], 12]): To what extent the characters of the irreducible representations of a nilpotent Lie groupN determine all central tempered distributions onN. A hereditary property is proved, which enables us to give a negative answer for a large class of nilpotent Lie groups. However, we give a positive answer for a certain series of two-step nilpotent groups. Furthermore, proving a generalisation of the Schwartz Kernel Theorem we decide the question specially for all groups of dimension<5.