@Article{Arlinskiĭ2011,
author = "Arlinskiĭ, Yury and Kovalev, Yury",
title = "Operators in divergence form and their Friedrichs and Kreĭn extensions",
journal = "Opuscula Math.",
year = "2011",
volume = "31",
number = "4",
pages = "501--517",
doi = "http://dx.doi.org/10.7494/OpMath.2011.31.4.501",
url = "http://dx.doi.org/10.7494/OpMath.2011.31.4.501",
abstract = "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.",
keywords = "symmetric operator, divergence form, Friedrichs extension, Kreĭn extension",
issn = "1232-9274"
}