Reich S., Shoikhet D. — Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Reich S., Shoikhet D. — Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces

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Название: Nonlinear Semigroups, Fixed Points, and Geometry of Domains in Banach Spaces

Авторы: Reich S., Shoikhet D.

Аннотация:

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces. Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 354

Добавлена в каталог: 17.06.2008

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Предметный указатель

(continuously) invertible operator      28
(Nonlinear) resolvent      190
Accumulation point      3
Adjoint operator      66
Admissible curve      83 86 93 95
Algebra with involution      66
Angular derivative      124 132 281
Angular limit      124
Approximate semigroup property      177 189 191
Approximating curve      130 229 231
Attractive point      266
Attractive sink point      263
Banach algebra      28
Banach Contraction Principle      108
Banach space      13.
Boundary      4
Boundary flow invariance condition      206
Boundary point      3
Bounded homogeneous polynomial      27
Brouwer's theorem      110
C*-algebra      66
Caratheodory pseudometric      89—91 97
Cartan's uniqueness theorem      71
Cauchy      12
Closure      3
Closure point      3
Cluster point      3
Common fixed point      220
Commutative algebra      28
Commuting family      220
Compact commuting property (CCP)      222
Compact open topology      61
complete      213
Complex extreme point      59
Composition operation      28 44
Continuity of scalar product      15
Continuous flows      157
Continuous semigroup      175
Continuous spectrum      31
Contraction      45
Convex closure      18
Convex hull      17
Curve, asymptotically normal      132 281
Denjoy — Wolff iteration property (DWIP)      224
Denjoy — Wolff point      137
Denjoy — Wolff theorem      119 126
Distance      9
Domain, homogeneous      100
Domain, p-hyperbolic      100
Domain, spiral-shaped      301
Dtationary point      219 223 270
Duality mapping      48 306
Earle — Hamilton theorem      206
Edelstein      109
Eigensubspace      31
Eigenvalue      31
Eigenvector      31
Elliptic automorphism      119 162
Equicontinuous family      41
Exponential type      270 272
Extreme point      18 58
Extreme subset      18
Fixed point      107
Flow invariance condition      199 201 202 213
Fractional linear transformation      162 166
Frechet derivative      51
Fundamental sequence      12
Gauge      20 38
Geodesic segment      87
Hausdorff      3
Hausdorff's maximality theorem      7
Hilbert space      15
Hille — Yosida theorem      173 196 206
Holomorphic, retract      146
Holomorphic, retraction      146
Homogeneous polynomial of order m      27
Hyperaccretive      49
Hyperbolic automorphisms      162
Hyperbolic domain      100
Hyperbolic length      87
Hyperbolic metric      101 257
Hyperbolic type      125 135
Implicit approximation property      231
Indefinite metric      163 164
Infinitesimal Caratheodory pseudometric      95
Infinitesimal Finsler metric      93
Infinitesimal Finsler pseudometric      93
Infinitesimal generator      160 175 215
Infinitesimal Poincare metric      86 95 164
Interior flow invariance condition      207
Interior point      3
Intersection      17
Involution property      73
Isometry      23 81 158
J*-algebra      67
Julia number      132
Julia — Caratheodory theorem      124 131 282 283
Julia — Wolff — Caratheodory theorem      125 131 135 280 285 286
Julia's lemma      122 123 282 284 285
Kobayashi pseudometric      91
Krein space      163 164
l-analytic function      68
Length      94
Limit point      3
Linear functional      8 22
Lipschitz constant      44
Locally convex space      21
Locally uniformly attractive fixed point      119 163 253
Lumer — Phillips theorem      173 174 204—206
Mapping k-contraction      108
Mapping m-linear      25
Mapping, biholomorphic      69
Mapping, bounded      23
Mapping, continuous      5
Mapping, contractive      109
Mapping, differentiable      51
Mapping, fixed point free      127
Mapping, holomorphic      54
Mapping, holomorphically accretive      203 205
Mapping, holomorphically conservative      203
Mapping, holomorphically dissipative      203 205
Mapping, Lipschitzian      44
Mapping, locally Lipschitzian      44
Mapping, monotone      48
Mapping, multilinear      25
Mapping, nonexpansive      45 108
Mapping, power convergent      119
Mapping, strongly accretive      48
Mapping, strongly monotone      48
Maximum Modulus Principle      57
Mazur's theorem      18
Mean ergodic theorem      41

Metric      8
Metric domain      193
Metric space      8
Metric topology      9
Minkowski functional      20
Moebius transformation      88 120
Montel space      12
Multiplicative      69
Neighborhood      1
Neighborhood base      3
Nontangential approach region      124
Norm      20
Norm of a linear operator      23
Normed space      13
Null point      25
Numerical range      202 203
One-parameter group      158 159
One-parameter groups of automorphisms      162
One-parameter semigroup      158
One-parameter semigroup of composition operators      166
One-parameter, continuous semigroup      158
One-parameter, discrete group      158
One-parameter, discrete semigroup      158
Operator, accretive      48 49 159 173
Operator, bounded      23
Operator, conservative      174 215
Operator, continuously invertible      28
Operator, dissipative      173
Operator, hermitian      66
Operator, m-accretive      49 240
Operator, strongly accretive      49 257
Operator, unbounded      23
Orthogonality      15
Parabolic automorphisms      163
Parabolic type      125
Parallelogram identity      15
Periodic point      220 223
Poincare metric      82 85 88—90 92 95 97 292
Point spectrum      31
Poutryagin space      164
Producing function      69
Product formula      189
Pseudohyperbolic distance      81
Pseudometric      89
Quasi-regular, fixed point      144
Quasi-regular, null point      299
Quasi-regular, point      239
radiaL      18
Range condition      190 193 194
Reflexive      34
Regular fixed point      144 148
Regular null point      239 299
Relative topology      5
Residual spectrum      31
Resolvent      30 49
Resolvent identity      190 192
Resolvent set      29
Restricted limit      132
Riesz — Dunford integral      68
Scalar product      14
Schwarz inequality      15
Schwarz lemma      76 209
Schwarz — Pick Inequality      77 122
Schwarz — Pick Lemma      81 162
Schwarz — Pick system      97 257
Self-mapping      44
Semi-complete vector field      213 298
Semigroups of fractional linear transformations      164
Seminorm      12
Separated      3
Sequentially compact      6
Set, absorbing      18
Set, balanced      18
Set, circled      18
Set, closed      2
Set, compact      6
Set, complete      12
Set, convex      17
Set, cover of      6
Set, dense      4
Set, diameter of      9
Set, open      1
Set, partially ordered      7
Set, relatively compact      6
Set, starshaped      300
Set, symmetric      19
Sink point      125 233 270 281
Space, compact      6
Space, complex      59
Space, conjugate      33
Space, dual      33 34
Space, locally convex      41
Space, metrizable      8
Space, real      18
Space, separable      4
Spectral mapping theorem      65
Spectrum      29
Spirallike mapping      301
Spirallike mapping on $\mathcal{D}$ with respect to an interior point      301
Spirallike mapping with respect to a boundary point      301
Star-shaped about zero      19
Starlike function      302
Starlike mapping      300
Starlike mapping with respect to a boundary point      300
Starlike mapping with respect to an interior point      300
Stolz angle      124
Strict contraction      45 108
Strictly inside      102
Strictly regular point      251 253 257 299
Strong maximum modulus principle      57 60
Strongly accretive      261
Strongly p-monotone      262
Strongly semi-complete      257 309
Strongly semi-complete vector field      262 290
Topological space      1
Topological vector space      8
topology      1
Topology of locally uniform convergence over V      60
Topology of uniform convergence on compact subsets      61
Topology, generated by the family of seminorms      21
Totally ordered      7
Uniform convergence      25
Uniform operator topology      25
Uniformly continuous semigroup      160 172
Uniformly Lipschitzian      45
unique      220
Unital -algebra      68
Vector space      7
Volterra integral operator      32
Weak maximum modulus theorem      57
Weak topology      34 35
Wolff — Schwarz Boundary Lemma      122
Wolff's point      125

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