Revision #292 → #1554 · back to history
addedSelf-adjoint operator5e63f6695f49
addedFinite-dimensional spectral theorem4e5c0bc93244
addedHamiltonian operator5b8c931ad515
addedSelf-adjoint iff unitarily equivalent to multiplication3df18d9d4508
addedGraph and extension of an operator7cb2ef327f48
addedAdjoint operatorf7a7936b8e4e
addedSymmetric (Hermitian) operatore673d057d1ad
addedSymmetric operators are closablef89e6c64766b
addedSelf-adjoint operator01d57e9741d8
addedEssentially self-adjoint operator0a0d6166f0e2
addedHellinger–Toeplitz theorem8c3df039fae2
addedBounded self-adjoint operator7df4b1abf78d
addedComplex form of a bounded operatorb6fc8991e92f
addedPositive bounded operators are self-adjoint1f3c47c4540d
addedInvertibility criterionea2a23273abf
addedOperator norm formulae1e5de954745
addedEigenvalues real, eigenvectors orthogonalc0cdc9c56d78
addedCompact self-adjoint operators have an eigenvalue912faac96405
addedResolvent setfdfe143298dc
addedSpectrumd70a7705f9b0
addedSpectrum of self-adjoint operator is real954f8a459064
addedBounded normal: real spectrum iff self-adjointb0d626fde816
addedBounded below481effbac499
addedSelf-adjoint operator has real spectrum06d5e55a872f
addedSymmetric operator with real spectrum is self-adjointe3bf468d2b43
addedSpectral theorem (informal)91412d3dd406
addedMultiplication operator0c508f99a068
addedMultiplication operators are self-adjointbc1d86bd4803
addedUnitary equivalence of operatorseac94b474ba5
addedUnitary equivalence preserves boundedness/self-adjointnessb64726ca4fed
addedSpectral theorem for bounded and unbounded operators12fa6691d1d3
addedSpectrum equals essential range96805bba15b5
addedSelf-adjoint operator is unitarily equivalent to a multiplication operator235d6747ca62
addedFunctional calculusee08dcda12f3
addedFunctional calculus of the Hamiltonian0e6255699b61
addedResolution of the identity66b86d590676
addedStieltjes integral representation of T47d5c7c0d06a
addedDirac notation for the spectral theoremf8353a2769e7
addedResolution of unityc7257128239f
addedBiorthogonal basis setd53164e64e5c
addedSymmetric operator with orthonormal eigenbasise913e216efc7
addedA is symmetric0adf1d5a0190
addedEigenfunctions are sinusoidsa3eb43e0485f
addedA has a compact inversefec9af74d524
addedPure point spectrum criterion6cc38d4d5666
addedHarmonic oscillator Hamiltonian4bc9f1f554bb
addedMomentum operator on an interval1efe6faa1edf
addedNo boundary conditions: not symmetric8f0469751344
addedDirichlet conditions: symmetricb12b9fe56679
addedDirichlet conditions: not essentially self-adjoint3d731a9488ef
addedPeriodic conditions: essentially self-adjointcda01056dfc9
addedSingular potential operator not essentially self-adjointd6db9fd8f328
addedAdjoint is not symmetric3c65a6c80edb
addedStone's theorem95c4bdcd7304
addedSchrödinger operator essential self-adjointness range13867972a83e
addedNo self-adjoint momentum operator on a half-linef5fcd830a131
addedD is symmetric0c3211caa5c4
addedSolution spaces are 1-dimensional274c95685f8b
addedD is not essentially self-adjointe7cf5e2622b2
addedSingle boundary condition: essentially self-adjoint879149dbd08c
addedSelf-adjoint extensions of symmetric differential operators711fab8aa5ac
addedConstant-coefficient operator is essentially self-adjoint58511d2313ba
addedFormal adjointc22d0126adad
addedFourier conjugate of P(D) is multiplication by P7af76af2139d
addedAdjoint is restriction of distributional formal adjointe74384cc308d
addedUniform multiplicity6d659db882e6
addedMutually singular measuresc54d8e45b014
addedUniqueness of the representationfe6e2d0dae0b
addedDirect sum multiplication representationede1f09fcce2
addedUniqueness of the direct-integral representation85e93f2b60c8
addedSpectral multiplicity functionc2214fd7b574
addedClassification of self-adjoint operatorse104a7edbcca
addedDirect-integral spectral theoremfbda86884255
addedThe Laplacian operatorb6e7144ff409
addedUniform multiplicity of the Laplacianada6a5cfc267