Kreyszig E. — Introductory functional analysis with applications :: Электронная библиотека попечительского совета мехмата МГУ

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Kreyszig E. — Introductory functional analysis with applications

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Название: Introductory functional analysis with applications

Автор: Kreyszig E.

Аннотация:

Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 688

Добавлена в каталог: 12.09.2007

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Предметный указатель

      11
      118
, $\bar{B}(x; r)$       18
      226
      11 25
      34 271
      411
      17 36 52 61 106 134 329 333 342
$C^{-}$       22 28 51 395
$c^{-}_{z}$       70 126 255
$C^{1}[a, b]$       110
$C^{2}[a, b]$       357
$C^{n}$       6 33 52 60 131
      110
      118
$l^{1}$       61 121 243
$L^{2}$       11 52 106 133 154 194 265 409
$L^{2}(-\infty, +\infty)$       562 573
$L^{2}[a, b]$       62 132
$L^{p}$       11 23 35 61 122 133 261
$L^{p}[a, b]$       62
$l^{\infty}$       6 22 33 61
$R\lambda(T)$       378
$r\sigma(T)$       378
      9 63
      18
$x^{*}$       106
      120
$\bar{d}(x, y)$       3
$\delta_{jk}$       114
$\epsilon$ -neighborhood      19
$\epsilon$ -net      412
$\mathbf{Q}$       29 37
$\mathbf{R}$       5 22 28 51 395
$\mathbf{R}^{n}$       6 33 52 60 121 131
$\mathcal{D}{T)$       83
$\mathcal{E}= (E\lambda)$       494
$\mathcal{G}(T)$       292
$\mathcal{N}(T)$       83
$\mathcal{R}(T)$       83
$\rho(T)$       371
$\sigma(T)$       371
$\sigma_{c}(T)$       371
$\sigma_{p}(T)$       371
$\sigma_{r}(T)$       371
Abelian algebra      394
Absolute convergence      68
Abstract function      613
Abstract space      1
Accumulation point      21
Adjoint Hilbert      196 236
Adjoint operator      232 416
Adjoint space      120
Algebra      394
Algebraic complement      146
Algebraic dual space      106
Algebraically reflexive      109 115
Alternating set      345
Analytic function      386
Annihilator      126 148 194 238 239
Appolonius’ identity      135
Approximate eigenvalues      545
Approximation      327
Ascoti’s thorem      454
Associated Laguerre polynomials      604
Associated Legendre functions      602
Augmented matrix      450
Axiom of Choice      211
Axioms for a metric      3
Axioms for a norm      59
Axioms for a topology      19
Axioms for a vector space      50
Axioms for an inner product      129
Baire category theorem      247
Ball      18
Banach algebra      395
Banach fixed point theorem      300 303
Banach space      58
Banach — Steinhaus theorem      246 249
Basis      55 68
Basis, dual      114
Basis, for a normea space      68
Basis, for a vector space      55
Basis, Hamel      55 211
Basis, orthonormal      168
Basis, Schauder      68
Bessel inequality      157 169
Best approximation      328
Bidual space      239
Bijection, bijective      615
Bilinear form      191
Binary relation      618
Biorthogonal system      444
Bohr radius      604
Bolzano — Weierstrass theorem      620
Boundary      24
Bounded inverse theorem      286
Bounded linear extension      100
Bounded linear functional      104 188 225
Bounded linear operator      91
Bounded sequence      26
Bounded sesquilinear form      191
Bounded set      16 26 66
Bounded variation      225
Canonical basis      54
Canonical embedding      108
Canonical mapping      108 240
Cartesian product      612
Category      247
Category theorem      247
Cauchy convergence criterion      620
Cauchy determinant      343
Cauchy sequence      28
Cauchy — Schwarz inequality      14
Cayley transform      556
Center of an algebra      398
Ces $\grave{a}$ ro summabiiity method      214 275
Chain      210
Characteristic determinant      365
Characteristic equation      365
Characteristic polynomial      365
Chebyshev approximation      336
Chebyshev polynomials      348
Closable operator      537
Closed ball      18
Closed extension      297
Closed graph theorem      292
Closed linear operator      292 535
Closed set      18 30
Closed subspace      30
Closure of a set      21 30
Closure of an operator      537
Codimension      57
Coefficient field      51
Column sum criterion      314
Commutative algebra      394
Commutator      578
Commuting operators      90 561
Compact      77
Compact, countably      619
Compact, extension      415
Compact, locally      82
Compact, metric space      77
Compact, operator      405
Compact, relatively      406
Compact, sequentially      619
Compact, set      77 619
Compact, topological space      619
Compactness of unit ball      80
Comparable elements      210

Compatible norm      102
Complement      609
Complementary pair of subspaces      146
Complete inner product space      128
Complete metric space      28
Complete normed space      59 73
Complete orthonormal sequence      168
Complete orthonormal set      168
Completely continuous operator      405
Completeness of spaces,       34
Completeness of spaces,       36
Completeness of spaces, $l^{p}$       35
Completeness of spaces, $l^{\infty}$       33
Completeness of spaces, $\mathbf{C}^{n}$       33
Completeness of spaces, $\mathbf{R}^{n}$       33
Completion of a metric space      41
Completion of a normed space      69
Completion of an inner product space      139
Complex -dimensional space $\mathbf{C}^{n}$       6 33 52 60 131
Complex plane $\mathbf{C}$       6 22 28 395
Complex vector space      51
Composition of mappings      616
Conjugate exponents      12
Conjugate linear      130 191
Conjugate space      120
Continuity of a norm      60
Continuity of an inner product      138
Continuity of vector space operations      70
Continuous extension      100
Continuous functional      104
Continuous functions      7 36 38
Continuous mapping      20 25 30 81
Continuous operator      96
Continuous spectrum      371
Continuous, completely      405
Contraction      300 303
Convergence, absolute      68
Convergence, in metric spaces      25
Convergence, in normed spaces      67
Convergence, of a sequence      25 67 620
Convergence, of a series      68
Convergence, of numerical integration processes      278
Convergence, strong      256 266
Convergence, strong operator      264
Convergence, uniform      37
Convergence, uniform operator      263
Convergence, weak      257 266
Convergence, weak operator      264
Convergence, weak ${}^{*}$       266
Convex function      334
Convex set      65 143 331
Convex strictly      332
Coset      57
Countable set      612
Countably compact      619
Cover, covering      618
Cross product      85
De la Vall $\acute{e}$ e — Poussin theorem      343
de Morgan’s laws      612
Decomposition of unity      494
Decreasing sequence of operators      473
Deficiency index      562
Definite integral      105
Degenerate kernel      457
Dense      21
Densely defined      527
Diameter of a set      16
Difference of projections      487
Difference of sets      609
Differential equation      315
Differentiation operator      84 93 294 567
Dimension, Hilbert      168 173
Dimension, of a vector space      55
Dimension, orthogonal      168
Direct method      307
Direct sum      146 433
Discrete metric      8 22
Discrete spectrum      371
Distance between points      4
Distance between sublets      16
Distance from a subspace      142
Distance function      3
Divergent sequence      269
Division algebra      403
Domain in the complex plane      386
Domain of a mapping      613
Domain of an operator      83
Dot product      85 105 131
Dual basis      114
Dual space      120
Dual space, algebraic      106
Eigenfunction      372
Eigenspace      365 372
Eigenvalue      364 366
Eigenvector      364 372
Embedding      109 241
Empty set      609
Equality of operators      99
Equicontinuity      454
Equivalence relation      618
Equivalent norms      75 291
Euclidean metric      5 6
Euclidean plane $\mathbf{R}^{2}$       5
Euclidean space $\mathbf{R}^{n}$       6 33 52 60 121 131
Euler formulas      160
Euler summabiiity method      275
Existence theorem for best approximations      328
Existence theorem for differential equations      315
Existence theorem for fixed points      300
Existence theorem for minimizing vectors      144
Existence theorem for splines      358
expansion      68
Extension ,proper      616
Extension of a functional      117 214 219 221
Extension of a mapping      616
Extension of an operator      99 297 526
Extension problem      2 3
Extremal point      337 338
Extreme point      336
Factor space      57
Family of sets      617
Finite dimensional normed space      72 96 111
Finite dimensional subspace      73
Finite dimensional vector space      54
Finite rank      408
Finite set      612
First category      247
Fixed point      299 323
Fourier coefficients      157 165
Fourier series      160 251
Fredholm alternative      451
Fredholm integral equation      319
Fredholm theorems      442
Fredholm theory      405
Frobenius theorem      469
Frontier      24
Function space      7
Functional      103
Functional, bounded linear      104
Functional, linear      104
Functional, positive homogeneous      214
Functional, relation      613
Functional, subadditive      214
Functional, sublinear      213
Fundamental orthonormal set      168
Fundamental sequence      28
Fundamental set      168
Gauss — Seidel iteration      311
GENERATED      53
Generating function      186 187

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