Quantum-mechanical models in $R_n$ associated with extensions of the energy operator in a Pontryagin space

The paper describes self-adjoint extensions of the operator $H_0=-\Delta$ from the Hilbert space $L_2(R_n)$ to a certain Pontryagin space generated by “interactions” represented by generalized functions. Hamiltonians of quantum-mechanical models are obtained by restricting such extensions to positive invariant subspaces.