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searching for Self-adjoint operator 38 found (122 total)

Eta invariant (342 words) [view diff] exact match in snippet view article find links to article

Dirichlet eta function. They also later used the eta invariant of a self-adjoint operator to define the eta invariant of a compact odd-dimensional smooth

Singular value (1,528 words) [view diff] exact match in snippet view article find links to article

square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator T ∗ T {\displaystyle T^{*}T} (where T ∗ {\displaystyle T^{*}} denotes

Symmetrizable compact operator (1,384 words) [view diff] exact match in snippet view article find links to article

composed with a positive operator with trivial kernel to produce a self-adjoint operator. Such operators arose naturally in the work on integral operators

Spectral triple (1,944 words) [view diff] exact match in snippet view article find links to article

a Hilbert space, an algebra of operators on it and an unbounded self-adjoint operator, endowed with supplemental structures. It was conceived by Alain

Bicommutant (410 words) [view diff] exact match in snippet view article find links to article

operator algebras. Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C*-algebra B(H), for some Hilbert space H, then the

Quantum statistical mechanics (1,233 words) [view diff] exact match in snippet view article find links to article

of a quantum mechanical system. A is given by a densely defined self-adjoint operator on H. The spectral measure of A defined by EA⁡(U)=∫UdλE⁡(λ),{\displaystyle

Affiliated operator (800 words) [view diff] exact match in snippet view article find links to article

the positive self-adjoint operator |A| should be affiliated with M. However, by the spectral theorem, a positive self-adjoint operator commutes with

Expectation value (quantum mechanics) (1,890 words) [view diff] exact match in snippet view article

A\rangle _{\sigma }} . Mathematically, A {\displaystyle A} is a self-adjoint operator on a separable complex Hilbert space. In the most commonly used

Stokes operator (486 words) [view diff] exact match in snippet view article find links to article

A−1{\displaystyle A^{-1}} of the Stokes operator is a bounded, compact, self-adjoint operator in the space H:={u→∈(L2(Ω))n|divu→=0 and γ(u→)=0}{\displaystyle

Quantization (physics) (1,488 words) [view diff] exact match in snippet view article

attempt is made to associate a quantum-mechanical observable (a self-adjoint operator on a Hilbert space) with a real-valued function on classical phase

Dirac operator (1,251 words) [view diff] exact match in snippet view article find links to article

of smooth, square-integrable functions. It can be extended to a self-adjoint operator on that domain. The square, in this case, is not the Laplacian,

Dixmier trace (632 words) [view diff] exact match in snippet view article find links to article

the Dixmier trace is an example of a non-normal trace. A compact self-adjoint operator with eigenvalues 1, 1/2, 1/3, ... has Dixmier trace equal to 1.

Kadison transitivity theorem (371 words) [view diff] exact match in snippet view article find links to article

Ax_{j}=y_{j}} . If B x j = y j {\displaystyle Bx_{j}=y_{j}} for some self-adjoint operator B {\displaystyle B} , then A {\displaystyle A} can be chosen to

Weitzenböck identity (832 words) [view diff] exact match in snippet view article find links to article

∇ {\displaystyle \Delta '=\nabla ^{*}\nabla } . This is another self-adjoint operator and, moreover, has the same leading symbol as the spin Laplacian

Complexification (Lie group) (7,216 words) [view diff] exact match in snippet view article

and the operator p can be written uniquely as p = exp T with T a self-adjoint operator. By the functional calculus for polynomial functions it follows

Functional analysis (2,492 words) [view diff] exact match in snippet view article find links to article

analysis. Spectral theorem — Let A {\displaystyle A} be a bounded self-adjoint operator on a Hilbert space H {\displaystyle H} . Then there is a measure

Momentum operator (2,031 words) [view diff] exact match in snippet view article find links to article

a Hermitian operator (more technically, in math terminology a "self-adjoint operator") when it acts on physical (in particular, normalizable) quantum

Partial trace (2,045 words) [view diff] exact match in snippet view article find links to article

trace TrW(T) is defined to be this operator. The partial trace of a self-adjoint operator is defined if and only if the partial traces of the positive and

Separation of variables (3,415 words) [view diff] exact match in snippet view article find links to article

and S {\displaystyle S} . If T {\displaystyle T} is a compact, self-adjoint operator on the space L 2 [ 0 , l ] {\displaystyle L^{2}[0,l]} along with

Symmetric cone (16,607 words) [view diff] exact match in snippet view article find links to article

operator L(a) being a positive self-adjoint operator on E. C is a convex cone in E because positivity of a self-adjoint operator T— the property that its eigenvalues

Supersymmetric quantum mechanics (3,121 words) [view diff] exact match in snippet view article find links to article

isn't necessarily linear in x. To avoid this problem, define the self-adjoint operator F = ℜ { W } {\displaystyle F=\Re \{W\}} . Then, [ Q , x } = − i

Dirac delta function (13,792 words) [view diff] exact match in snippet view article find links to article

Hilbert space, for example, the normalized eigenvectors of a compact self-adjoint operator, any vector f can be expressed as f = ∑ n = 1 ∞ α n φ n . {\displaystyle

Ilya Prigogine (2,714 words) [view diff] exact match in snippet view article find links to article

mapping of each linear operator into Liouville space, yet not every self-adjoint operator of Liouville space has a counterpart in Hilbert space, and in this

Robert S. Doran (1,819 words) [view diff] exact match in snippet view article find links to article

Academic Press, 1988. ISBN 0-12-252722-4 Self-adjoint and non-self-adjoint operator algebras and operator theory, (ed.) vol. 120, Contemporary Mathematics

Coherent states in mathematical physics (5,762 words) [view diff] exact match in snippet view article find links to article

structure of these objects as superpositions of eigenstates of some self-adjoint operator, as was the harmonic oscillator Hamiltonian for the standard CS

Belavkin equation (3,159 words) [view diff] exact match in snippet view article find links to article

{i}{\hbar }}H\right)\psi dt+L\psi dy} Here, L{\displaystyle L} is a self-adjoint operator (or a column vector of operators) of the system coupled to the external

Divergent series (4,997 words) [view diff] exact match in snippet view article find links to article

applications, the numbers ai are sometimes the eigenvalues of a self-adjoint operator A with compact resolvent, and f(s) is then the trace of A−s. For

Quantum graph (2,937 words) [view diff] exact match in snippet view article find links to article

+B\mathbf {f} '=\mathbf {0} .} The matching conditions define a self-adjoint operator if ( A , B ) {\displaystyle (A,B)} has the maximal rank d {\displaystyle

Sturm–Liouville theory (4,692 words) [view diff] exact match in snippet view article find links to article

satisfy the above regular boundary conditions. Moreover, L is a self-adjoint operator: ⟨ L f , g ⟩ = ⟨ f , L g ⟩ . {\displaystyle \langle Lf,g\rangle

Paneitz operator (2,349 words) [view diff] exact match in snippet view article find links to article

{\displaystyle J} . The operator P 4 {\displaystyle P_{4}} is a real self-adjoint operator. On CR manifolds like S 3 {\displaystyle S^{3}} where the Webster-Tanaka

Complete set of commuting observables (3,841 words) [view diff] exact match in snippet view article find links to article

_{n}\rangle \}} be a complete set of orthonormal eigenkets of the self-adjoint operator A {\displaystyle A} corresponding to the set of real-valued eigenvalues

Uniformly bounded representation (3,555 words) [view diff] exact match in snippet view article find links to article

cannot be unitarizable, since otherwise D would be similar to a self-adjoint operator. Jacques Dixmier asked in 1950 whether amenable groups are characterized

Hilbert transform (7,691 words) [view diff] no match in snippet view article find links to article

{\displaystyle L^{p}(\mathbb {R} )} . The Hilbert transform is an anti-self adjoint operator relative to the duality pairing between L p ( R ) {\displaystyle

CR manifold (5,615 words) [view diff] exact match in snippet view article find links to article

Laplacian ◻ b {\displaystyle \Box _{b}} is a non-negative, formally self-adjoint operator. It is degenerate and has a characteristic set where its symbol

Hamiltonian constraint of LQG (6,931 words) [view diff] exact match in snippet view article find links to article

_{b}M-M\partial _{b}N)/(\det(q))} As we know in the loop representation a self-adjoint operator generating spatial diffeomorphisms. Therefore, it is not possible

Arithmetic Fuchsian group (3,844 words) [view diff] exact match in snippet view article find links to article

{\displaystyle S} is compact it extends to an unbounded, essentially self-adjoint operator on the Hilbert space L 2 ( S ) {\displaystyle L^{2}(S)} of square-integrable

Schwarz triangle (10,972 words) [view diff] exact match in snippet view article find links to article

from the observation of Paul Halmos and others, that the positive self-adjoint operator (S – T)2 commutes with both S and T. In the case above, however

De Broglie–Bohm theory (16,633 words) [view diff] exact match in snippet view article find links to article

space, and the potential in Schrödinger's equation becomes a local self-adjoint operator acting on that space. The field equations for the de Broglie–Bohm