SOME REMARKS ON KREIN EXTENSION THEORY

The extension problem of semibounded symmetric operators and symmetric operators with a pp is studied in detail. Using a suitable representa tion (Krein model) for the inverses of those operators a parameterizat ion of their symmetric and self-adjoint extensions is introduced which improves Krein's famous extension theory. In particular, the paramete rization clearly shows which self-adjoint extensions in the gap case c orrespond to Friedrichs and v. Neumann or Krein extensions in the semi bounded case. Moreover, special properties of the extensions as the ex actness of the gap are characterized in terms of the parameters.