In mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence...
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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...
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Lumer–Phillips theorem 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...
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unitary equivalence. By Stone's theorem, there is a one-to-one correspondence between self-adjoint operators and (strongly continuous) one-parameter unitary...
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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...
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Unitarity (physics) (redirect from Unitary (physics))
Born rule Probability axioms Quantum channel Stone's theorem on one-parameter unitary groups Wigner's theorem Ouellette, Jennifer. "Alice and Bob Meet the...
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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...
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_{i}\}} has no finite accumulation point. Resolvent set Stone's theorem on one-parameter unitary groups Holomorphic functional calculus Spectral theory Compact...
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Fuglede's theorem Compression (functional analysis) Friedrichs extension Stone's theorem on one-parameter unitary groups Stone–von Neumann theorem Functional...
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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...
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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...
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Stone's theorem on one-parameter unitary groups (functional analysis) Stone–Tukey theorem (topology) Stone–von Neumann theorem (functional analysis, representation...
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Self-adjoint operator (redirect from Hahn-Hellinger theorem)
operators. By Stone's theorem on one-parameter unitary groups, self-adjoint operators are precisely the infinitesimal generators of unitary groups of time evolution...
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systems, especially in the context of the Stone–von Neumann theorem. More generally, one can consider Heisenberg groups associated to n-dimensional systems...
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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...
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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...
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Stone–Weierstrass theorem, Stone's representation theorem for distributive lattices, Stone duality, Stone's theorem on one-parameter unitary groups,...
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Fourier transform (redirect from Fourier shift theorem)
Fourier transform exist. For example, one uses the Stone–von Neumann theorem: the Fourier transform is the unique unitary intertwiner for the symplectic and...
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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...
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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...
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Ergodic flow (redirect from Ambrose−Kakutani theorem)
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...
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Hilbert space (section Operators on Hilbert spaces)
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...
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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...
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Bound state (section Node theorem)
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...
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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...
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Quaternion (section Lagrange's four-square theorem)
to be discovered. According to the Frobenius theorem, the algebra H {\displaystyle \mathbb {H} } is one of only two finite-dimensional division rings...
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Danskin's theorem — used in the analysis of minimax problems Maximum theorem — the maximum and maximizer are continuous as function of parameters, under...
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John von Neumann (section Topological groups)
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...
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Pi (category Commons category link is on Wikidata)
of unitary characters of T. That is, continuous group homomorphisms from T to the circle group U(1) of unit modulus complex numbers. It is a theorem that...
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mean-field theory, where neglecting higher-order fluctuations in order parameter allows interaction terms to be replaced with quadratic terms, obtaining...
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