This coalescence is, on principle, different from the well-known degeneration of two eigenstates of a
Hermitian operator H.
We say that T [member of] B(E) is a
Hermitian operator if T [member of] H(B(E)).
where b is the vector storing the measured data, and the superscript H denotes the
Hermitian operator. Due to the ill-posedness of the problem, the above summation is terminated early, say at the index K.
Given a
Hermitian operator M on a vector space V with a subspace U [subset or equal to] V, let [pr.sub.U]: V [right arrow] U denote the orthogonal projection, and then denote by [M.sub.U] the
Hermitian operator on U given by [M.sub.U] = [pr.sub.U] [omicron] M [omicron] [pr.sub.U].
Some other specific subjects which I found interesting were related to the iterative method for computing the square root for a positive
Hermitian operator [6, p.
Taking into account that the Hamiltonian is a
Hermitian operator, it is possible to show that for n [not equal to] 1:
Weyl [20] examined the spectra of all compact perturbations of a
hermitian operator on Hilbert space and found in 1909 that their intersection consisted precisely of those points of the spectrum which were not isolated eigenvalues of finite multiplicity.
We show that every
Hermitian operator [??] in the spherical symmetric problem ([??] = R-1[??] R) can be written in the form
Observations of the unstable particle can be also described in the quantum-logical language of yes-no questions, like "Do we see the unstable particle?" and an observable, which can take two values 1 or 0, corresponding to the possible answers "yes" or "no." Obviously, the
Hermitian operator of this observable is the projection T introduced above.
Since the Hamiltonian is a
Hermitian operator, one concludes that if the Hilbert space basis yields a non-diagonal Hamiltonian matrix then the lowest eigenvalue "favors" eigenfunctions that are a linear combination of the Hilbert space basis functions.
H.Weyl [22] examined the spectra of all compact perturbations of a
hermitian operator on Hilbert space and found in 1909 that their intersection consisted precisely of those points of the spectrum which were not isolated eigenvalues of finite multiplicity.
The difference in the resolvents of two self-adjoint extensions of the non-densely defined
Hermitian operator A = -[Laplacian operator] (when restricted to an appropriate subspace of [L.sup.2](0,x)) is studied by explicitly constructing a Green's function solution.
; in this case, K(x, y) is called a Hermitian kernel. The concept of Hermitian operators may be extended to unbounded linear operators in a Hilbert space.