The von Neumann problem for nonnegative symmetric operators

We develop a new approach and present an independent solution to von Neumann's problem on the parametrization in explicit form of all non-negative self-adjoint extensions of a densely defined nonnegative symmetric operator. Our formulas are based on the Friedrichs extension and also provide a description for closed sesquilinear forms associated with nonnegative self-adjoint extensions. All basic results of the well-known Krein and Birman-Vishik theory and its complementations are derived as consequences from our new formulas, including the parametrization (in the framework of von Neumann's classical formulas) for all canonical resolvents of nonnegative self-adjoint extensions. As an application all nonnegative quantum Hamiltonians corresponding to point-interactions in R-3 are described.