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| Davies E. — Spectral Theory and Differential Operators |
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| Предметный указатель |
Adams 67
Almost analytic 24
Banach algebras 22
Band, in spectrum 96
Bessel function 61 130
Biharmonic 113
boundary conditions 1
Cauchy’s Theorem 28
Cayley transform 11
Centre of mass 162
Coefficients, discontinuous 123
Coefficients, measurable 135
Coefficients, variable 118
Compact metric space 75
Convergence, norm resolvent 41
Convergence, strong 39
Convex region 117
Convolution 46
Coordinate neighbourhood 143
Cusp 146
Cyclic vector 34
Davies ix 22
Deficiency index 12
Deficiency subspace 12
Degree 45
Dieudonne vii
Diffeomorphism 142
Dinchlet boundary conditions 118 120
Dinchlet Laplacian 127
Dinchlet problem ix 99
Dirac delta function 53
Distance function 107
distribution 53 121
Domain 2
Double well 171
Eigenfunction 2
Eigenfunction, boundary decay 136
Eigenspace 73
Eigenvalue 2
Eigenvalue, isolated 73
Eigenvalues, computation of 150
Eigenvalues, monotonicity of 136
Eigenvalues, of ball 130
Eigenvalues, of cube 127
Eigenvalues, of sector 131
Elastic membrane 99 118 140
Elastic plate 113
Electrostatic potential 99
Elliptic regularity theorem 133
Energy, ground state 155
Energy, kinetic 155
Energy, potential 155
Energy, total 155
Essential range 16
Essentially self-adjoint 8
Extension 2
Extension operator 145
Extension property 146
Finite element method 151
Fluid flow 140
Form closure 83
Form core 83
Form, closable 83
Form, closed 83
Form, quadratic 81
Form, semibounded 156
Form, sesquilinear 81
FOURIER vii
Fourier transform 49
Fractional powers 79
Friedrichs 86
Friedrichs extension 86
Functional calculus 24
Gelfand 22
Gram — Schmidt 36
Graph 3
Green 11
Green function 94
Ground state 1SS
Haar measure 106
hadamard 64
Hamiltonian 188
Hardy 104
Hardy inequality 104
Harmonic function 134
Heat equation 99 118 140
Helfler 22
Helfler — Sjostrand formula 24
Helium atom 163
hilbert vii
Hilbert — Schmidt operator 97
Hydrogen atom 163
Ideal of operators 97
interactions 161
Interpolation 63
Interval arithmetic 96
Isometric extension 11
Kato 19
Kufner 104
Laplace 11
Laplace — Beltrami operator 119
Laplacian 11
Lax 86
legendre 110
Legendre polynomial 10
Legendre’s equation 10 110
Liebnitz formula 26
Lipschitz boundary 146
Lipschitz condition 124
Locally  156
Lower semicontinuous 82
| Matrix, sparse 152
Matrix, tridiagonal 35
Milgram 86
Modifier 46
Monomial 48
Multi-index 45
Multi-index, degree of 45
Neumann boundary conditions 140
Neumann Laplacian 147
Neumann, von 22
Norm analytic 4
Operator, adjoint 7
Operator, biharmonic 113
Operator, closable 6
Operator, closed 3
Operator, closure 6
Operator, compact 66 75
Operator, conjugation 14
Operator, differential 57
Operator, divergence form 119
Operator, essentially self-adjoint 8
Operator, extension 2
Operator, finite rank 75
Operator, Hilbert — Schmidt 67
Operator, isometric 11
Operator, linear 2
Operator, local 71
Operator, multiplication 15
Operator, non-negative 78
Operator, real 14
Operator, resolvent 4
Operator, Schrodinger 155
Operator, self-adjoint 8
Operator, semibounded 78
Operator, singular elliptic 109
Operator, symmetric 6
Opic 104
Orthogonal complement 8
Partition of identity 144
periodic structure 96
Perturbation 17
Perturbation, compact 166
Perturbation, relatively bounded 17
Poincare vii
Poisson problem 99
Polynomial 48
Potential 155
Potential, chemical 118
Potential, local singularities 159
Product of Banach spaces 3
Projection 40
Projection, spectral 41
Pseudodistance 107
Quantum theory 155 161
Rayleigh 88
Rayleigh — Ritz formula 88
Regular region 107
Relative bound 17
Rellich 19
Residue theorem 31
Resolvent equations 4
Riemann — Lebesgue lemma 49
Riemannian manifold 119
Riesz 75
Riesz representation theorem 37
Ritz — Galerkin method 100
Schrodinger 155
Schwartz 52
Schwartz space 45
Self-adjoint 8
Semigroup 101
Separable 8
Simon 156
Singular elliptic 109
Sjostrand 22
Smooth 11 45
Sobolev 52
Sobolev space 67 124
Spectral theorem 32
Spectrum 4
Spectrum, discrete 73
Spectrum, essential 73 167
Spectrum, negative 168
Spectrum, point 73
Spectrum, positive 164
Spin 155
Square root 80
Statistics 155
Stokes’ formula 26
Stone 22
Stone — Weierstrass theorem 32
Sturm — Liouville operator 94
Subspace, cyclic 34
Subspace, invariant 33
Subspace, spectral 41
Symbol 58
Symbol, principal 59
Taylor’s Theorem 30
Tempie — Lehmann formula 95
Three lines lemma 64
Threshold 169
Translation invariance 57
Triangulation of region 151
Turbine blade 113
Uniform ellipticity 60
Unitary equivalence 36
Unitary group 44
Variational formulae 88
Vertex of region 131
Weak derivative 54 121
Zorn’s Lemma 35
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