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Operators in divergence form and their Friedrichs and Krein extensions

Arlinskii Y., Kovalev Y.

Opuscula Mathematica

2011

Vol. 31, no. 4

501-517

For a densely defined nonnegative symmetric operator A = L*(2)L1 in a Hilbert space, constructed from a pair L1 ⊂ L2 of closed operators, we give expressions for the Friedrichs and Krein nonnegative selfadjoint extensions. Some conditions for the equality (L*(2)L1)* = L*(1)L2 are obtained. Applications to 1D nonnegative Hamiltonians, corresponding to point interactions, are given.