Curtain R.F., Pritchard A.J. — Functional Analysis in Modern Applied Mathematics :: Электронная библиотека попечительского совета мехмата МГУ

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Curtain R.F., Pritchard A.J. — Functional Analysis in Modern Applied Mathematics

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Название: Functional Analysis in Modern Applied Mathematics

Авторы: Curtain R.F., Pritchard A.J.

Язык:

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 339

Добавлена в каталог: 09.04.2005

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Предметный указатель

      89
$L_{\infty}(E)$       34
$\mathcal{L}(E)$       33
$\mathcal{L}(X)$       40
$\mathcal{M}^2$ space      148
Absolute continuity      32
Abstract equations      146
Adjoint dynamical system      247
Adjoint operator      66 71
Affine subset      6
Algebraic dual      45
Almost everywhere      30
Almost everywhere, nowhere      86
Alternative theorem      102
Analytic semigroups      158
Approximate controllability      308
Approximation theory      292
Arzela — Ascoli theorem      109
Asymptotic stability      195
Asymptotically stable semigroup      193
B      88
Banach space      18
Banach’s Closed Graph Theorem      45
Bang-bang control      250
Basis (Hamel)      7
Bijective      8
Bilinear      66
Binomial distribution      76 80
Bochner integral      88
Bolzano — Weirstrass property      16
Borel algebra      12
Borel algebra, measurable functions      28
Borel algebra, measurable space      24
Borel algebra, sets      24
Boundary value problem      161
Boundary value problem, variation      50
Bounded sequence      16
Bounded sequence, set      15
Bounded sequence, transformation      39
Brownian motion      85
Calculus in a Banach space      87
Caratheodory theorem      122
Cauchy distribution      81
Cauchy distribution, sequence      16
Cayley — Hamilton theorem      223
Characteristic function      28
Classical solution      134
Closed      5
Closed operator      45
Closed operator, set      15
Closure      15
Coercive      66
Compact normal resolvent      179
Compact normal resolvent, operator      53
Compact normal resolvent, space      109
Compact normal resolvent, support      19
Compactness      15
Complete measure space      27
Completeness      18
Condition number      283
Conditional compactness      16
Conditional probability      82
Conjugate gradient      304
Continuity      12 108
Continuity for continuous time stochastic processes      85
Continuity, equi      109
Continuity, strong      43
Continuity, uniform      42
Continuous functions C[a, b]      9
Continuous functions C[a, b], linear functional      46
Continuous functions C[a, b], random variable      80
Continuous functions C[a, b], spectrum      163
Continuous functions C[a, b], time stochastic process      82
Contraction mapping      20
Contraction mapping, Mapping Theorem      20
Control of a diffusion equation      326
Controllability      221 308
Controllability, matrix      222
Controllability, space      221
Convergence      108
Convergence in probability      78
Convergence of random variables      78
Convergence of sequences      14
Convergence of series      14
Convergence with probability      1 78
Convergence, quadratic      290
Convergence, strong      42
Convergence, uniform      42
Convergence, weak      51
Convergence, weak*      52
Convex, balanced, absorbing set      110
Covariance function      78
Delta function      46 136
Dense subspaces of $L_p(-\infty, \infty)$       35
Denseness      20
Diagonally dominant      285
Differential delay equations      130 329
Differentiation of a distribution      137
Differentiation of a distribution, under the integral      33
Diffusion equation      133
DIMENSION      7
Dirichlet problem      161 185
Discrete random variable      79
Discrete random variable, stochastic process      82
Distributed parameter systems      307
distribution      136
Distribution, function      27 76 79
Distribution, theory      136
Domain of an operator      44
Dominated Convergence Theorem      90
Dual space      47
Duality      231
Eberlein — Shmulyan Theorem      52
Eigenspaces      162
Eigenvectors      162
Elliptic differential equations      133 141
Equi continuity      109
Equivalence classes      34
Essential surpremum      34
Euclidean space      3
Euler — Lagrange equations      260
Expectation      31 77
Exponential distribution      81
Extended Fundamental Theorem      32
Extension Principle      44
Extremal controls      247
Fatou’s Lemma      30
Feedback control      227
Filtering      234
Finite measure space      26
Fixed point      20
Fourier coefficients      61
Fourier coefficients, expansion      61
Frechet derivative      97
Frechet derivative, space      112
Fredholm alternative theorem      176
Fredholm Alternative Theorem, integral equation      160 177
Fubini — Tonnelli Theorem      33 90
Fundamental matrix      126
Fundamental matrix, Theorem of Calculus      31
Gateaux derivative      95
Gaussian elimination      284
Gaussian elimination, random variable      81
Gaussian elimination, stochastic process      83
Generalized inverse function theorem      262
Generalized Lagrange Multiplier Theorem      262
Gradient methods      300
Gram — Schmidt orthogonalization process      60
Graph of a Linear Operator      44
Gronwell’s lemma      124

Hahn — Banach theorem      46 113
Hamiltons principle      260
Hausdorff space      108
Hermite polynomials      61
Hilbert space      56
Hille — Yosida theorem      153
Holder continuous      158
Holder continuous, inequality      48
Hyperbolic differential equation      133
Hyperplane      6
Independent events      81
Infinite dimensional      7
Infinite dimensional systems theory      307
Infinitesimal generator of a semigroup      150
Inhomogencous abstract equations      119 156
Injective      73
Inner product      55
Inner product, space      55
Integrable function      29
Integral of non-negative measurable functions      29
Integral of non-negative measurable functions, Riccati equation      320
Integration on $(\pi,\mathcal{P}, \mu)$       29
Integration theory for real valued functions      24
Invariant set      203
Inverse (algebraic)      38
Invertibility      39
Isometrically isomorphic      11
Isometry      11
Isomorphic linear vector spaces      8
Jacobi polynomials      61
Joint distribution function      82
Kalman — Bucy Filter Theorem      240
Kuhn — Tucker conditions      269
La Salle’s Theorem      204
Laguerre polynomials      61
Laplaces equation      133 183 185
Lax — Milgram Theorem      65
Least squares minimization      257
Lebesgue integral on $\mathcal{R}^k$       30
Lebesgue integral on $\mathcal{R}^k$ , measurable functions      28
Lebesgue integral on $\mathcal{R}^k$ , measure      25
Lebesgue integral on $\mathcal{R}^k$ , Stieltje’s integral      31
Lebesgue integral on $\mathcal{R}^k$ , Stieltje’s measure space      26
Lebesgue — Banach space      34
Lebesgue — Banach space, Dominated Convergence Theorem      30 90
Lebesgue — Banach space, integrable      18 24
Legendre polynomials      7 61
Liapunov functional      195
Liapunov functional, stability      195
Limit point      15
Linear dependence      6
Linear dependence, functionals      45
Linear dependence, independence      6
Linear dependence, manifold      5
Linear dependence, quadratic problem      253
Linear dependence, stochastic differential equations      129
Linear dependence, subspace      5
Linear dependence, systems      125 198 220
Linear dependence, topological space      110
Linear dependence, transformation      37
Linear dependence, variety      5
Linear dependence, vector space      3
Liouville’s theorem      170
Lipschitz assumption      21 120
Lipschitz assumption, function      32
Local extrema      253
Locally convex space      111
Lower semicontinuity      53
Markov process      84
Maxima      96
Maximal      6
Maximal orthonormal sequence      61
Maximum principle      247
Mean square convergence      78
Mean Value Theorems      102
Measurable function      28
Measurable function, set      24
Measurable function, space      24
Measure space      25
Metric space      107
Mild evolution operator      216
Mild evolution operator, solution      159
Minimisation of bilinear forms      254
Minimisation of bilinear forms, under equality constraints      261
Minimisation of bilinear forms, with inequality constraints      267
Minkowski functional      111
Minkowski functional, inequality      9 10 34
Natural embedding      50
Neighbourhood      108
Neighbourhood, basis      108
Newton’s method      289
Nonlinear ordinary differential equations      119
Nonlinear ordinary differential equations, programming      267
Nonlinear ordinary differential equations, systems      201
Norm      3
Norm of a linear bounded operator      39
Normal distribution      81
Normal distribution, operator      69
Normed linear space      3 8
Numerical methods      282
Numerical methods, solution of optimization problems      299
Observability      229 230 313 314
Open balls      107
Open balls, covering      109
Open balls, loop control      227
Open balls, Mapping Theorem      44 113
Open balls, set      15 106
Optimal control theory      271
Optimal control theory, filter      240
Optimization problems      253
Ordinary differential equations      117
Orthogonal complement      58
Orthogonal complement, projection      58
Orthogonal complement, Projection Theorem I      64 235
Orthogonal complement, Projection Theorem II      293
Orthogonality      57
Orthonormal set      59
p-Norm      9 14
Parabolic differential equations      133 142
Parallelogram law      56
Parseval equality      62
Partial differential equations      132
Perturbation theory      191 205
Pettis integral      87
Picard — Lindeloff Theorem      120
Point spectrum      163
Pontryagin’s maximim principle      277
Positive limiting set, $\gamma^+$       203
Positive limiting set, $\gamma^+$ , operator      69
Principle of superposition      37
probability density      80
Probability density, space      27
Probability density, theory      75
Product of normed spaces      11
Quadratic convergence      290
Quadratic convergence, cost control problems      315
Quadratic convergence, functionals      302
Quadratic convergence, programming      269
Quasi-evolution operators      218
Random variable      28 76
Range of an operator      44
Realization theory      251
Reflexive space      50
Regular point      261
Regulator problem      265
Relative boundedness      206
Relative boundedness, compactness      16
Relative boundedness, topology      106
Residual spectrum      163
Resolution of identity      58 174

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