Opuscula Mathematica
Opuscula Math. 31, no. 4 (2011), 501-517

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.
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Yury Arlinskiĭ
East Ukrainian National University, Department of Mathematical Analysis, Kvartal Molodyozhny 20-A, Lugansk 91034, Ukraine
Yury Kovalev
East Ukrainian National University, Department of Mathematical Analysis, Kvartal Molodyozhny 20-A, Lugansk 91034, Ukraine
About the article ▼
Received: 2011-01-26.
Revised: 2011-02-21.
Accepted: 2011-02-22.
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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.
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