TY  - JOUR
ID  - Arlinskiĭ2011
LB  - Arlinskiĭ2011
AU  - Arlinskiĭ, Yury
AU  - Kovalev, Yury
TI  - Operators in divergence form and their Friedrichs and Kreĭn extensions
ST  - Operators in divergence form and their Friedrichs and Kreĭn extensions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2011
VL  - 31
IS  - 4
SP  - 501
EP  - 517
DO  - http://dx.doi.org/10.7494/OpMath.2011.31.4.501
UR  - http://dx.doi.org/10.7494/OpMath.2011.31.4.501
AB  - For a densely defined nonnegative symmetric operator \(\mathcal{A} = L_2^*L_1 \) in a Hilbert space, constructed from a pair \(L_1 \subset L_2\) of closed operators, we give expressions for the Friedrichs and Kreĭn 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.
KW  - symmetric operator
KW  - divergence form
KW  - Friedrichs extension
KW  - Kreĭn extension
SN  - 1232-9274
ER  -