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A Characterization of Positive Self-Adjoint Extensions and Its Application to Ordinary Differential Operators

Guangsheng Wei and Yaolin Jiang
Proceedings of the American Mathematical Society
Vol. 133, No. 10 (Oct., 2005), pp. 2985-2995
Stable URL: http://www.jstor.org/stable/4097913
Page Count: 11
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A Characterization of Positive Self-Adjoint Extensions and Its Application to Ordinary Differential Operators
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Abstract

A new characterization of the positive self-adjoint extensions of symmetric operators, T0, is presented, which is based on the Friedrichs extension of T0, 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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