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Let be the symmetric operator given by the restriction of to , where is a self-adjoint operator on the Hilbert space and is a linear dense set which is closed with respect to the graph norm on , the operator domain of . We show that any self-adjoint extension of such that can be additively decomposed by the sum , where both the operators and take values in the strong dual of . The operator is the closed extension of to the whole whereas is explicitly written in terms...
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