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
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.
- 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
- Received: 2011-01-26.
- Revised: 2011-02-21.
- Accepted: 2011-02-22.
