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| Pazy A. — Semigroups of linear operators ans applications to PDE |
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| Предметный указатель |
 -group 22
-semigroup 4
A-admissible subspace 122
A-priori estimates 212
Adjoint operator 38
Adjoint resolvent 38
Adjoint semigroup 39
Adjoint strongly elliptic operator 212
Alternating directions 93
Analytic semigroup 60
Backward difference approximation 93
Cauchy problem, linear autonomous 100
Cauchy problem, linear nonautonomous 105 126 134
Cauchy problem, quasilinear 200
Cauchy problem, semilinear 183
Compact semigroup 48
Contraction semigroup 8
Convergence of infinitesimal generators 88
Convergence of semigroups 85
Convergence of solutions as  119 174
Decay of evolution systems as 173
Decay of semigroups as 116
Differentiable semigroup 51
Dissipative operator 13
Distribution semigroup 252
Domain of infinitesimal generator 1 5
Dual semigroup 38
Duality set 13
Embedding of semigroup in group 24
Equation, heat 98 234
Equation, higher order 253
Equation, Korteweg-de Vries 247 252
Equation, parabolic 225 261
Equation, Scroedinger 238 241
Equicontinuous semigroup 252
Evolution system 129
Exponential formula 21 32 33 92
Fractional powers of operator 72
Fractional steps 93
Gagliardo — Nirenberg's inequality 242
Garding's inequality 209
Graph norm 190
Group 22 see
Heat equation, linear 98
Heat equation, nonlinear 234
Hille — Yosida theorem 8
Hoelder continuous function 112
Hyperbolic evolution system 135
Hyperbolic initial value problem 105 134
Implicit difference approximation 35
Inequality, Gagliardo — Nirenberg's 242
Inequality, Garding's 209
Inequality, Hausdorf — Young's 224 262
Inequality, Kallman — Rota's 7 253
Inequality, Landau's 8
Infinitesimal generator 1
Initial value problem, higher order 253
Initial value problem, linear autonomous 100
Initial value problem, linear nonautonomous 105 126 134
Initial value problem, non well posed 253
Initial value problem, quasilinear 200
Initial value problem, semilinear 183
Invariant subspace 121
Kallman — Rota's inequality 7 254
Korteweg — de Vries equation 247
Landau's inequality 8
Laplace transform 25
Locally Lipschitz function 185
Lumer — Phillips theorem 14
m-dissipative operator 81
Mild solution 106 146 168 184
Null space 36
Numerical range 12
Operator, adjoint 38
Operator, dissipative 13
Operator, m-dissipative 81
Operator, part of 39
| Operator, self adjoint 41
Operator, strongly elliptic 209
Operator, symmetric 41
Operator, unitary 41
Parabolic evolution system 150
Parabolic initial value problem 110 167 225
Part of operator in subspace 39
Perturbations by bounded operators 76
Perturbations by Lipschitz operators 184
Perturbations of generators of analytic semigroups 80
Perturbations of generators of contraction semigroups 81
Perturbations of stable families of generators 132
Positive semigroups 256
Post — Widder inversion formula 35
Pseudo resolvent 36
Quasilinear initial value problem 200
r-convergence 86
Renorming 17 18
Representation of semigroups 90
Resolvent identity 20
Resolvent operator 8
Resolvent set 8
Scroedinger equation, linear 223
Scroedinger equation, nonlinear 230
Self adjoint operator 41
Semigroup, 4
Semigroup, adjoint 39
Semigroup, analytic 60
Semigroup, bounded linear operators 1
Semigroup, compact 48
Semigroup, contractions 8
Semigroup, differentiable 51
Semigroup, distributions 252
Semigroup, equicontinuous 252
Semigroup, nonlinear 253
Semigroup, positive 256
Semigroup, strongly continuous 4 see
Semigroup, strongly measurable 255
Semigroup, uniformly bounded 8
Semigroup, uniformly continuous 1
Semigroup, weakly continuous 44 255
Semilinear initial value problem 183
Sobolev's imbedding theorem 208 222
Solution of initial value problem, classical 100 105 139
Solution of initial value problem, generalized 36 228
Solution of initial value problem, mild 106 146 168 184
Solution of initial value problem, strong 109
Solution of initial value problem, weak 258
Solution of initial value problem, Y-valued 140
Spectrum of semigroup 45
Spectrum of compact semigroup 51
Spectrum of differentiable semigroup 53
Spectrum, continuous 46
Spectrum, point 45
Spectrum, residual 46
Stable family of operators 130 200
Strong solution 109
Strongly elliptic operator 209
Strongly measurable semigroup 255
Taylor's formula for continuous functions 33
Theorem, Hille — Yosida 8 19
Theorem, Lumer — Phillips 14
Theorem, Sobolev 208 222
Theorem, Trotter — Kato 87
Uniformly bounded semigroups 8
Uniformly continuous semigroups 1 25 50
Uniqueness, evolution systems 135 145 160
Uniqueness, infinitesimal generator 3 6
Uniqueness, solution 101 106
Uniqueness, Y-valued solution 140 146
Unitary group 41
Unitary operator 41
Weak infinitesimal generator 42 43
Weak solution 258
Weakly continuous semigroups 44 255
Y-valued solution 140
Yosida approximation 9
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