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
Famous quotes containing the words von, neumann and/or formulas:
“Whoever speaks of Europe is wrong: it is a geographical expression.”
—Otto Von Bismarck (1815–1898)
“It means there are times when a mere scientist has gone as far as he can. When he must pause and observe respectfully while something infinitely greater assumes control.”
—Kurt Neumann (1906–1958)
“You treat world history as a mathematician does mathematics, in which nothing but laws and formulas exist, no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.”
—Hermann Hesse (1877–1962)