In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence...

being the group of unitary operators on a Hilbert space. See Stone's theorem on one-parameter unitary groups. In his monograph Lie Groups, P. M. Cohn...

{1}{\lambda }}.} Stone's theorem on one-parameter unitary groups Engel and Nagel Theorem II.3.8, Arendt et al. Theorem 3.3.4, Staffans Theorem 3.4.1 Engel...

Stone–Weierstrass theorem Stone–von Neumann theorem Stone's theorem on one-parameter unitary groups It may also refer to the theorem of A. H. Stone that for Hausdorff...

Born rule Probability axioms Quantum channel Stone's theorem on one-parameter unitary groups Wigner's theorem Ouellette, Jennifer. "Alice and Bob Meet the...

unitary equivalence. By Stone's theorem, there is a one-to-one correspondence between self-adjoint operators and (strongly continuous) one-parameter unitary...

Boolean algebras. Stone was the son of Harlan Fiske Stone, who was the Chief Justice of the United States in 1941–1946. Marshall Stone's family expected...

Schröder–Bernstein theorems for operator algebras (operator algebras) Stinespring factorization theorem (operator theory) Stone's theorem on one-parameter unitary groups...

Fuglede's theorem Compression (functional analysis) Friedrichs extension Stone's theorem on one-parameter unitary groups Stone–von Neumann theorem Functional...

operators. By Stone's theorem on one-parameter unitary groups, self-adjoint operators are precisely the infinitesimal generators of unitary groups of time evolution...

_{i}\}} has no finite accumulation point. Resolvent set Stone's theorem on one-parameter unitary groups Holomorphic functional calculus Spectral theory Compact...

the bounded functional calculus, one can prove part of the Stone's theorem on one-parameter unitary groups: Theorem— If A is a self-adjoint operator,...

U(t)=e^{-(i/\hbar )tH}} is a consequence of Stone's theorem on one-parameter unitary groups. It is assumed that H does not depend on time and that the perturbation...

The existence of the generator is guaranteed by the Stone's theorem on one-parameter unitary groups. In simpler terms, the total angular momentum operator...

systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to n-dimensional systems...

Stone–Weierstrass theorem, Stone's representation theorem for distributive lattices, Stone duality, Stone's theorem on one-parameter unitary groups,...

The famous spectral theorem holds for self-adjoint operators. In combination with Stone's theorem on one-parameter unitary groups it shows that self-adjoint...

extends to a unitary operator on L2(R), as asserted by Plancherel's theorem. Suppose U(s) and V(t) are one parameter unitary groups on a Hilbert space...

order parameter is not a conserved quantity, Nambu–Goldstone modes are typically massless and propagate at a constant velocity. An important theorem, due...

Neumann mean ergodic theorem states the following: If Ut is a (strongly continuous) one-parameter semigroup of unitary operators on a Hilbert space H, and...

understood in terms of the theory of unitary representations of locally compact groups: if Γ is the fundamental group of a closed surface, regarded as a...

t\right)=\left(-\xi ,x,te^{-i2\pi \xi x}\right).} According to the Stone–von Neumann theorem, the unitary representations ρ and ρ ∘ j are unitarily equivalent, so...

articles on operator theory, and the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary...

H} as the generator of the one-parameter unitary group ( W ( t f ) ) t ∈ R {\displaystyle (W(tf))_{t\in \mathbb {R} }} on the symmetric Fock space. These...

that the Stone–von Neumann theorem is formulated in terms of the Weyl relations. A discrete version of the Weyl relations, in which the parameters s and...

relations and act irreducibly on the Segal–Bargmann space, the Stone–von Neumann theorem applies. Thus, there is a unitary map B from the position Hilbert...

to be discovered. According to the Frobenius theorem, the algebra H {\displaystyle \mathbb {H} } is one of only two finite-dimensional division rings...

separable complex Hilbert space H {\displaystyle H} . Define a one-parameter group of unitary operators ( U t ) t ∈ R {\displaystyle (U_{t})_{t\in \mathbb...

Danskin's theorem — used in the analysis of minimax problems Maximum theorem — the maximum and maximizer are continuous as function of parameters, under...

Bob by acting on her system. Causality is thus preserved, in this particular scheme. For the general argument, see no-communication theorem. As mentioned...