A characterization of positive self-adjoint extensions and its application to ordinary differential operators

Wei, Guangsheng; Jiang, Yaolin

doi:10.1090/S0002-9939-05-07837-8

A characterization of positive self-adjoint extensions and its application to ordinary differential operators
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by Guangsheng Wei and Yaolin Jiang PDF

Proc. Amer. Math. Soc. 133 (2005), 2985-2995 Request permission

Abstract:

A new characterization of the positive self-adjoint extensions of symmetric operators, $T_0$, is presented, which is based on the Friedrichs extension of $T_0,$ a direct sum decomposition of domain of the adjoint $T_0^{*}$ and the boundary mapping of $T_0^{*}$. In applying this result to ordinary differential equations, we characterize all positive self-adjoint extensions of symmetric regular differential operators of order $2n$ in terms of boundary conditions.

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