Kovalov I. Nonnegative selfadjoint extensions and point interactions models

Symmetric operators which have a divergence representation and their nonnegative selfadjoint extensions are studied. A criteria for representation of a nonnegative symmetric operator in divergence form by use of an unbounded nonnegative symmetric operator and its nonnegative selfadjoint extension is given. A parameterization of all quasi-selfadjoint m-accretive and m-sectorial extensions of nonnegative symmetric operators in intrinsic terms is obtained. Description of all nonnegative Hamiltonians of point interaction models on a line, on a plane and in a space, and all quasi-selfadjoint m-accretive and m-sectorial Hamiltonians in the case of a line are given. The Riesz bases property of Dirac’s delta-functions in their linear spans is proved.