Operators in divergence form and their Friedrichs and Kreĭn extensions

Opuscula Mathematica

Yury Kovalev¹  Yury Arlinskiĭ¹ 

[1] East Ukrainian National University, Department of Mathematical Analysis, Kvartal Molodyozhny 20-A, Lugansk 91034, Ukraine;

关键词: symmetric operator;    divergence form;    Friedrichs extension;    Kreĭn extension;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2011.31.4.501

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown