%0 Journal Article
%T Operators in divergence form and their Friedrichs and Krein extensions
%A Yury Arlinskii
%A Yury Kovalev
%J Opuscula Mathematica
%D 2011
%I AGH University of Science and Technology
%X For a densely defined nonnegative symmetric operator $A = L_2^*L_1 $ in a Hilbert space, constructed from a pair $L_1 \subset L_2$ of closed operators, we give expressions for the Friedrichs and Krein nonnegative selfadjoint extensions. Some conditions for the equality $(L_2^* L_1)^* = L_1^* L_2$ are obtained. Applications to 1D nonnegative Hamiltonians, corresponding to point interactions, are given.
%K symmetric operator
%K divergence form
%K Friedrichs extension
%K Krein extension
%U http://www.opuscula.agh.edu.pl/vol31/4/art/opuscula_math_3135.pdf