Michelangeli, AlessandroOttolini, Andrea2016-06-162016-06-162016https://openscience.sissa.it/handle/1963/35195For quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the ``Ter-Martirosyan--Skornyakov condition'' gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.enPoint interactionsself-adjoint extensionsKrein-Visik-BIrman theoryTer-Martirosyan-Skornyakov operatorsPreprintMAT/0711/2016/MATE