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Engel K.-J., Nagel R. — Short Course on Operator Semigroups
Engel K.-J., Nagel R. — Short Course on Operator Semigroups

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Название: Short Course on Operator Semigroups

Авторы: Engel K.-J., Nagel R.

Аннотация:

The book gives a streamlined and systematic introduction to strongly continuous semigroups of bounded linear operators on Banach space. It treats the fundamental Hille-Yosida generation theorem as well as perturbation and approximation theorems for generators and semigroups. The special feature is its treatment of spectral theory leading to a detailed qualitative theory for these semigroups.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 260

Добавлена в каталог: 19.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $C_0$      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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