Opuscula Math. 31, no. 4 (2011), 501-517
http://dx.doi.org/10.7494/OpMath.2011.31.4.501

Opuscula Mathematica

# Operators in divergence form and their Friedrichs and Kreĭn extensions

Yury Arlinskiĭ
Yury Kovalev

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.

Mathematics Subject Classification: 47A20, 47B25, 47E05, 34L40, 81Q10.

Full text (pdf)

Yury Arlinskiĭ, Yury Kovalev, Operators in divergence form and their Friedrichs and Kreĭn extensions, Opuscula Math. 31, no. 4 (2011), 501-517, http://dx.doi.org/10.7494/OpMath.2011.31.4.501

a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.