The symmetric extensions of a closed symmetric operator " A " is in one-to-one correspondence with the isometric extensions of its Cayley transform " U A ".
22.
Now if time is a disturbance, essentially consisting of vibrations forwards then backwards, then the antisymmetric operators would cancel ( this is how I picture it ) and the symmetric operators would amplify.
23.
The self-adjoint extensions of a closed symmetric operator " A " is in one-to-one correspondence with the unitary extensions of its Cayley transform " U A ".
24.
An operator that has a unique self-adjoint extension is said to be "'essentially self-adjoint "', but a symmetric operator may have many or no self-adjoint extensions.
25.
Defined on the space of complex-valued C " functions on [ 0, 1 ] vanishing near 0 and 1 . " D " is a symmetric operator as can be shown by integration by parts.
26.
The fact that the master constraint operator \ hat { M } is densely defined on H _ { Diff }, it is obvious that \ hat { M } is a positive and symmetric operator in H _ { Diff }.
27.
In 1938 Naimark began his doctoral studies at the Steklov Institute of Mathematics, where he developed his renowned work on self-adjoint extensions of symmetric operators, and began a collaboration with Israel Gelfand that would last for over a decade.
28.
The domain of " A " is the space of all " L " 2 functions for which the right-hand-side is square-integrable . " A " is a symmetric operator without any eigenvalues and eigenfunctions.
29.
Contrary to what is sometimes claimed in introductory physics textbooks, it is possible for symmetric operators to have no eigenvalues at all ( although the compact inverse, meaning that the corresponding differential equation " Af " = " g " is solved by some integral, therefore compact, operator " G ".
30.
In fact this norm is equivalent to the operator norm on the symmetric operators ad " X " and each non-zero eigenvalue occurs with its negative, since i ad " X " is a " skew-adjoint operator " on the compact real form \ mathfrak { k } \ oplus i \ mathfrak { p }.
