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Hino Y., Murakami S., Naito T. — Functional Differential Equations with Infinite Delay
Hino Y., Murakami S., Naito T. — Functional Differential Equations with Infinite Delay

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Название: Functional Differential Equations with Infinite Delay

Авторы: Hino Y., Murakami S., Naito T.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 317

Добавлена в каталог: 15.08.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C (J \times X, Y)$      218
$C (S, \mathbb{E})$      8
$C^{c} (X, Y)$      215 218
$C^{\rho} (X, Y)$      215
$c_{00}$      5
$C_{0} (X)$      71
$C_{c} (X)$      71
$f^{\tau}$      8 218
$L_{\alpha} x$      264
$p_{\Omega}$      254
$r_{e} (T)$      124 135
$s.d.\Omega (u, F)$      261
$S_{0} (t)$      8
$T (t, \sigma)$      109
$u.a.s.l.\Omega_{F} (u)$      257
$u.a.s.\Omega_{F} (u)$      257
$u.s.\Omega_{F} (u)$      257
$UC (J \times X, Y)$      219
$U^{\bot \bot}$      204 see
$X^{\odot \odot}$      158
$X^{\odot}$      157
$x_{t}$      1
$Y^{\bot}$      146
$\alpha (T)$      124
$\alpha$, $\alpha_{L}$      130
$\alpha$-measure      125
$\alpha_{0}$      140
$\alpha_{\gamma} (\varphi)$      163
$\beta$      127 135 182 195
$\beta_{\nu}$      41
$\Delta (\lambda)$      138 196
$\Delta_{X}$      68
$\Gamma (X)$      85
$\gamma$      92 118 159
$\gamma_{i}$      118 159
$\hat{x}$      115
$\hat{\varphi}$      7
$\int_{{}_* J} f (t) dt$      117
$\mathbb{B}_{g}$      15
$\mathbb{C}$      4
$\mathbb{E}$      4
$\mathbb{R}$      4
$\mathbb{R}$-bounded      203
$\mathbb{R}$-bounded solution      255
$\mathscr{L}_{*}$      133
$\Omega (f)$      219
$\Omega (u)$      256
$\Omega (u, f)$      221
$\omega (\lambda)$      134
$\Omega_{G} (u)$      256
$\rho (f, g)$      215
$\rho (G, H)$      261
$\tau$-translation      218
$| \cdot |_{K}$      4
$| \cdot |_{X}$      4
Adjoint      111
Adjoint equation      102 111 212
Adjoint theory      156
Admissible      5 8
Almost periodic in t uniformly for $\varphi$      8 235 238 254
Almost periodic solution      254 257 258 261 273 274
AP      254
AS      192
Asymptotically almost periodic function      256 258 261
Basis vector      148
Borel prolongation of a Radon measure      88 92
Bounded measure      68
Bounded solution      203
Bounded variation      59
Browder's theorem      124 142 284
bv      164
Caratheodory condition      36
Caratheodory type mapping      92
Characteristic exponent of T (t, s)      178
Characteristic matrix      138 195
Characteristic multipliers of T (t, s)      178
Compact open topology      215
Compactly      4 219 256
Complex measure      68
Continuous dependence      43
Continuous in Lebesgue      85
Converge compactly      4 219 256
Darboux — Stieltjes integral      54
Diminishing function      229 239
Equation in the hull      219
Equicontinuous      215
Essential spectral radius      124
Essential spectrum      124
Ev XAS      227
Ev XS      226
Existence and uniqueness      35
Fading memory      7 32 189 191 194 198 244
Favard's theorem      273
Finite delay      1
Floquet type theorem      184
Fubini theorem      74
Functional differential equation of retarded type      1
Fundamental axioms      4
Fundamental decomposition      6
Fundamental matrix      102 104 197
Globally attracting      251
H (f)      218 254
H (u, f)      220
history      1
Hull      218 254
IAS      227
Indicator function      93
Infinite delay      1
Infinitesimal generator      130 150
Inherited property      222 224 238
Integrable in the weak-star topology      116
Integrodifferential equation      244 263
Invariance principle      241
IS      227
Jordan decomposition      59 70
Kato's example      225
Kneser's property      51
Kuratowskii's measure of noncompactness      124
Lebesgue continuous      85
Lebesgue Stieltjes measure      71
Lebesgue — Stieltjes integral      71
Levinger's theorem      142 288
Limiting equation      8 219 242
Linear almost periodic system      270 273
Linear autonomous system      130 195
Linear periodic system      177 182 203 211 273
Linear system      99
Linear Volterra equation      274
Locally finite measure      68
Locally of bounded variation      90
m (P)      36 53
MAs      227
Maximal solution      43
Measurable in the weak-star topology      116
Measure of noncompactness      124
Measure, bounded      68
Measure, complex      68
Measure, Dirac      68
Measure, Lebesgue — Stieltjes      71
Measure, locally finite      68
Measure, positive      68
Measure, Radon      85 92
Measure, real      68
Measure, regular Borel      68
Measure, regular complex Borel      68
mesh      36 53
Minimal hull      235
Minimal solution      271
ms      227
n-species system      244
Noncontinuable solution      43
Normal eigenvalue      124
Normal point      124 141
Normalized function      90 93
Nussbaum's theorem      125
Partition      36 53
Period map      177
Periodic equation or system      123 182 203 238 254 258
Periodic family      177 182
Periodic solution      211 254 259 273 275
Perturbed system      226 238
Phase space      1
Point spectrum      123
Polar representation      68 88
Positive measure      68
Positive orbit      198 255
Present state      5
Quotient phase space      7 118 122 162
Quotient space      7 115
Radon measure      85 93
Real measure      68
Reflexive      156
Reflexive, $\odot$-reflexive (sun-reflexive)      163
Regular Borel measure      23 68
Regular Borel prolongation of a Radon measure      89
Regular complex Borel measure      68
Regular function of bounded variation      60
Regular system      219 222 233 238
Resolvent      131
Resolvent set      123
Riemann — Stieltjes integral      54
Riesz representation theorem (Theorem 3.3.4)      90 92
S (t)      6
Second dual space      118
Semigroup      6
Separation condition      263 268
Separation constant      264
Solution, operator      109 182
Solution, semigroup      7 123 130
Space, $BC^{0}$      2
Space, $C \times L^{p} (g)$      15 23 151 155 191
Space, $C^{0}$      9
Space, $C^{\infty}$      9
Space, $C_{g}$      2 10 21 150
Space, $C_{g}^{0}$      2 10 150 190 195
Space, $C_{g}^{\infty}$      11 190 201
Space, $C_{\gamma}$      14 163 190
Space, $UC_{g}$      10 150 191
Space, $UC_{\gamma}$      163
Space, $\hat{\mathscr{B}}$      7 118
Space, $\mathbb{E} \times M$      19
Space, $\mathscr{B}$      4
Space, $\mathscr{B}^{*}$      110
Space, $\mathscr{B}^{\circ}$      210
Space, $\mathscr{B}_{0}$      8 125 188
Space, BC      2 9 187 251
Space, BL      175
Space, BU      9 175 254
Spectrum      123
Stability      192 215
Stability, asymptotic      192
Stability, asymptotic under X-perturbation      227 252
Stability, eventually asymptotic under X-perturbation      227
Stability, eventually under X-perturbation      226
Stability, exponential asymptotic      198
Stability, integral      227
Stability, integral asymptotic      227 238
Stability, M-      227
Stability, M-asymptotic      227 238
Stability, total      227
Stability, total asymptotic      227 238
Stability, under disturbances from $\Omega (u, F)$      261
Stability, under X-perturbation      227 251
Stability, under X-perturbation w.r.t. BC      251
Stability, uniform      192 274
Stability, uniform asymptotic      192
Stability, uniform asymptotic in $\Omega (F)$      222
Stability, uniform asymptotic in H (F)      222 235 238
Stability, uniform asymptotic in the large with respect to $\Omega_{F} (u)$      257
Stability, uniform asymptotic with respect to $\Omega_{F} (u)$      257
Stability, uniform in H (F) ($\Omega (F)$)      222
Stability, uniform with respect to $\Omega_{F} (u)$      257
Stability, weakly uniform asymptotic      192
Stability, weakly uniform asymptotic in $\mathbb{E}$      193
Stability, weakly uniform asymptotic in $\Omega (F)$      222
Stability, weakly uniform asymptotic in H (F)      222 235
Static continuation      6
Stieltjes integral      53
Strongly continuous semigroup      6
supp $\varphi$      5
T (f)      8 218
T (t)      59 123 130
t-section      1
t-segment of x      1
TAS      227
Total variation      59
Total variation of a complex measure      68 88
TS      227
Type number      131
UAs      192
UAS in H (F)      222
Uniform fading memory space      189 194 235
Uniformly attracting in $\Omega (F)$      233
Uniformly equicontlnuous      198 200 215
Unique for initial value problem with respect to $\Omega_{F} (u)$      266
Unique in $\Omega (F)$      233
Unsymmetric Fubini theorem      74
us      192
Variation of constants formula      99 105 106
Variation of constants formula in the second dual space      119
Volterra equation      2 51 274
w*-integrable on J      116
w*-measurable on J      116
w*-topology      156
Weak* Laplace transform      133
WUAS      192
WUAS in H (F) ($\Omega (F)$)      222
X*      115
X**      118
XAS      227
XAS w.r.t. BC      252
xs      227
XS w.r.t. BC      251
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