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| Авторизация |
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| Engel K.-J., Nagel R. — Short Course on Operator Semigroups |
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| Предметный указатель |
Abstract Cauchy Problems 1
Abstract, Cauchy problem See Cauchy problem
Abstract, extrapolation space 59
Abstract, Volterra operator 120
Adjoint operator 227
Algebra homomorphism 45
Approximate eigenvalue 160
Approximate eigenvector 160
Approximate point spectrum 160
Balanced exponential growth 215
Banach lattice 206
Boundary condition 173
Boundary spectrum 185 216
Calkin algebra 166
Cauchy problem 18 77 110 112 185 217
Cauchy problem, mild solution of 110
Cauchy problem, solution of 110
Cauchy problem, well-posed 113
Characteristic equation 173 202
Characteristic function 173
Chernoff product formula 150
Classical solution 110
Closed convex hull 223
Closure of an operator 226
Compact resolvent 107
Core of an operator 39 45 227
Delay differential equation 87 173
Derivation 45
Diffusion semigroup 53 55 131
Domain of an operator 36 40 229
Dominant eigenvalue 17 195 199
Duality set 81
Dynamical system 1
Dyson — Phillips series 121
Eigenvalue 159
Eigenvalue dominant 17 195 199
Eigenvector 159
Entire vector 74
Equilibrium point 194
Essential growth bound 197
Essential norm 166
Essential range 27
Essential spectral radius 166
Essential spectrum 165 166
Essential supremum 28
Extension of an operator 226
Extrapolation space 59
Flow 84 85
Formula, Chernoff product 150
Formula, Post — Widder 152
Formula, Trotter product 154
Formula, variation of parameter 120
Fredholm domain 166
Fredholm operator 166
Function, strictly positive 211
Function, subadditive 169
Gaussian semigroup 55
Generator 18 34 36 71
Graph 225
Graph, norm 39 225
Group, generator of 71
Group, induced by flow 85
Group, periodic 32
Group, rotation 32
Group, strongly continuous 2 71
Growth bound of a semigroup 5 168 188
Growth bound, essential 197
Hadamard formula 159
Heat semigroup 55
Initial value problem 110
Isolated singularities 164
Landau — Kolmogorov inequality 45
Left, translation 30
Linear form, strictly positive 211
Mild solution 110
Minimal polynomial 14
Multiplication operator 20 27
Multiplication semigroup 22 28 50 102
One-parameter group 12
One-parameter semigroup 12
Operator, adjoint 49 227
Operator, approximate eigenvalue of 160
Operator, approximate eigenvector of 160
Operator, approximate point spectrum of 160
Operator, bounded 227
Operator, closable 75 226
Operator, closed 225
Operator, closure 226
Operator, compact resolvent, with 107
Operator, core of 39
Operator, delay differential 86 173
Operator, differential 84
Operator, dissipative 75
Operator, domain of 36
Operator, eigenvalue of 159
Operator, Fredholm 166
Operator, Hille — Yosida 80
Operator, infinitely divisible 19
Operator, kernel of 226
Operator, local 30
Operator, multiplication 20 27
Operator, normal 26 100 184
Operator, part of 47 58 163
Operator, point spectrum of 159
Operator, range of 227
Operator, relatively bounded 124
Operator, relatively compact 132
Operator, residual spectrum of 161
Operator, resolvent of 41 157
Operator, resolvent set of 41 157
Operator, second-order differential 87
Operator, sectorial 90
Operator, self-adjoint 26 83 100
Operator, skew-adjoint 82
Operator, spectral bound of 44 168
Operator, spectral decomposition of 162
Operator, spectrum of 41 157
Operator, Volterra 120
Operator, weakly closed 226
Orbit map 2 35
Perturbation, additive 115 124
Point spectrum 159
Pole 165
Pole, algebraic multiplicity of 165
Pole, algebraically simple 165
Pole, first-order 165
| Pole, geometric multiplicity of 165
Post — Widder inversion formula 152
Principle of uniform boundedness 224
Pseudoresolvent 138
RANGE 43 227
Residual spectrum 161
Residue 165
Resolvent 34 157
Resolvent map 157
Resolvent map, isolated singularities of 164
Resolvent map, poles of 165
Resolvent map, residue of 165
Resolvent, compact 107
Resolvent, equation 157
Resolvent, integral representation 42
Resolvent, pseudo 138
Resolvent, set 34 157
Riemann — Lebesgue lemma 230
Right translation 30
Rotation group 32
Semiflow 89
Semigroup,  2
Semigroup, abstract Sobolev space of 57 59
Semigroup, adjoint 9
Semigroup, analytic 95
Semigroup, asymptotically norm-continuous 185
Semigroup, balanced exponential growth, with 215
Semigroup, bounded 5
Semigroup, contractive 5
Semigroup, differentiable 104
Semigroup, diffusion 53 55 131
Semigroup, eventually compact 107
Semigroup, eventually differentiable 104
Semigroup, eventually norm-continuous 104
Semigroup, extrapolation space of 59
Semigroup, fixed space 194
Semigroup, generator of 34
Semigroup, growth bound of 5 168
Semigroup, hyperbolic 191
Semigroup, immediately compact 107
Semigroup, immediately differentiable 104
Semigroup, immediately norm-continuous 104
Semigroup, irreducible 212
Semigroup, isometric 5
Semigroup, matrix 12
Semigroup, multiplication 22
Semigroup, nilpotent 32
Semigroup, norm-continuous 18
Semigroup, positive 206
Semigroup, product 9 49
Semigroup, quasi-compact 196
Semigroup, quasi-contractive 68
Semigroup, quotient 9 48
Semigroup, rescaled 8 47
Semigroup, strongly continuous 2
Semigroup, strongly stable 186
Semigroup, subspace 9 47
Semigroup, translation 32
Semigroup, type of 5
Semigroup, uniformly continuous 18
Semigroup, uniformly exponentially stable 186
Semigroup, uniformly stable 186
Semigroup, weak* generator of 49
Semigroup, weak*-continuous 9
Semigroup, weak*-stable 188
Semigroup, weakly continuous 5
Semigroup, weakly stable 186
Semigroups, isomorphic 8
Similar 8 14 46
Sobolev space, abstract 57 59 62
Sobolev tower 60
Solution, classical 110
Solution, mild 110
Spectral bound 44 168
Spectral bound, equal growth bound condition 177
Spectral decomposition 162
Spectral inclusion theorem 179
Spectral mapping theorem 161 176
Spectral mapping theorem for eventually norm-continuous semigroups 182
Spectral mapping theorem for the point spectrum 180
Spectral mapping theorem for the residual spectrum 180
Spectral mapping theorem for the resolvent 161
Spectral mapping theorem, circular 193
Spectral mapping theorem, weak 176
Spectral projection 162
Spectral radius 158
Spectral theorem 27
Spectrum, approximate point 160
Spectrum, essential 165 166
Spectrum, point 159
Spectrum, residual 161
Stability condition 144 154
Stability, strong 186
Stability, uniform 186
Stability, uniform exponential 186
Stability, weak 186
Stability, weak* 188
Strong operator topology 224
Support of a function 21
Tensor product 230
Theorem, Banach — Alaoglu 223
Theorem, Gearhart — Greiner — Pruess 189
Theorem, Hille — Yosida 66
Theorem, Krein 223
Theorem, Liapunov 189
Theorem, Lumer — Phillips 76
Theorem, Stone 82
Theorem, Trotter — Kato 141 144
Topology, strong operator 224
Topology, uniform operator 224
Topology, weak 223
Topology, weak operator 224
Topology, weak* 223
Translation group 30
Translation property 89
Translation semigroup 30–32
Trotter product formula 154
Uniform operator topology 224
Variation of parameter formula 120
Vector lattice 205
Volterra operator 120
Weak operator topology 224
Weak spectral mapping theorem 176
Weak topology 223
Weak* generator 49
Weak* topology 223
Yosida approximation 66 136 145
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