Von Neumann's Formulas
Suppose A is symmetric; any symmetric extension of A is a restriction of A*; Indeed if B is symmetric
Theorem. Suppose A is a densely defined symmetric operator. Let
Then
and
where the decomposition is orthogonal relative to the graph inner product of dom(A*):
These are referred to as von Neumann's formulas in the Akhiezer and Glazman reference.
Read more about this topic: Self-adjoint Operator
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