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

Geometric multiplicity      369
Geometric series      375
Gershgorin’s theorem      313
Gram determinant      353
Gram — Schmidt process      157
Graph      292
Group      621
H $\ddot{o}$ lder inequality      14
H $\ddot{o}$ lder summahility method      274
Haar condition      337
Haar uniqueness theorem      340
Hadamard determinant theorem      356
Hadamard formula      392
Hahn — Banach theorem      214 219 221
Half space      111
Hamel basis      55 211
Hamilton operator      591
Hamming distance      9
harmonic oscillator      585 589 594
Heisenberg commutation relation      579
Heisenberg uncertainty principle      580
Hellinger — Toeplitz theorem      525
Helmholtz equation      584
Hermite polynomials      180 587
Hermitian form      195
Hermitian matrix      203 368
Hermitian operator      201 460
Hilbert dimension      168 173
Hilbert relation      379
Hilbert sequence space $l^{2}$       11 52 106 154 194 265 409
Hilbert space      128 352 459
Hilbert space isomorphism      173
Hilbert-adjoint operator      196 236 527
Holomorphic function      386
Holomorphic operator function      387
Holomorphic, locally      387
Homeomorphism      46
Homomorphism      84
Hydrogen atom      603
Hypergeometric function      351
Hyperplane      111 224
Idempotent      148 385
Identity of an algebra      395 402
Identity operator      84 93
Image      613
Incomparable elements      210
Incomplete normed spaces      61
Inconsistent equations      344
Increasing sequence of operators      473
Index set      617
Induced metric      4 59
inf      619
Infinite dimensional      54
Infinite sequence      see Sequence
Infinite series      see Series
Initial value probieir      315
Injection, injective      86 614
Inner product      128
Inner product space      128
Integral equation      319 405 453
Integral operator      84 94 454
Interior      19
Interior point      19 331
Interlacing of zeros      351
Interpolation      357
Intersection      609
Invariant subspace      374 491
Inverse      396 622
Inverse image      613
Inverse mapping      87 615
Inverse operator      87 101
Invertible element      396 399
Isometric      41
Isomorphism      108
Isomorphism, Hilbert space      173
Isomorphism, inner product space      139
Isomorphism, metnc space      108
Isomorphism, normed space      120
Isomorphism, vector space      109
iterated kernel      325 456
Iteration      302 310 311
Jacobi iteration      310 314
Kernel, degenerate      457
Kernel, iterated      325
Kernel, of an integral equation      319
Kernel, of an operator      83
kernel, resolvent      325
Kronecker delta      114
Laguerre polynomials      184
Laplacian      584
Lattice      213
Least squares approximation      336
Lebesgue integral      62
Left-shift operator      555
Legendre differential equation      180 603
Legendre polynomials      176
LIMIT      25 257 264
Limit point      21
linear combination      53 72
Linear dependence      53
Linear equations      307
Linear extension      117
Linear functional      104
Linear hull      see Span
Linear independence      53
Linear operator      82
Linear space      50
Lipschitz condition      307 315
Locally compact      82
Locally holomorphic      387
Mapping      613
Mapping, continuous      20
Matrix      85 95 102 202 234 364 396
Maximal element      210
Maximally symmetric      535
Meager      247
Metric      3
Metric space      3
Metric, induced by a norm      59
Minimizing vector      144
Minkowski inequality      14
Momentum operatoi      576
Monotone sequence of operators      473
Multiplication operator      84 511 562
Multiplicity      369
Natural injection      152 617
Natural norm      103
Negative part of an operator      498
Neighborhood      19
Neumann series      324 455
Newton’s methoa      305
Nilpotent operator      393
Nonmeage      247
Norm      59 105
Norm of a functional      104
Norm of a sesquilinear form      191
Norm of an operator      92
Norm on a product space      292 296
Normal matrix      203
Normal operator      201
Normally solvable      438
Normed algebra      395
Normed linear space      58
Normed space      58
Normed vector space      58
Nowhere dense      247
Null operator      see Zero operator
Null space      83 98 110
Numerical integration      276
Observable      575

One-to-one      86— 614
Open ball      18
Open covering      619
Open mapping      286
Open mapping theorem      286
Open set      18
Operator      82
Operator, adjoint      232 516
Operator, bounded linear      91
Operator, compact      405
Operator, equations      436
Operator, function      387
Operator, Hilbert adjoint      196 236
Operator, linear      82
Operator, normal      201
Operator, of finite rank      408
Operator, resolver      370
Operator, self-adjoint      201 459 534
Operator, symmetric linear      333
Operator, unitary      201 205 546
Ordered set      210
Orthogonal      131
Orthogonal complement      146
Orthogonal dimension      168
Orthogonal matrix      203
Orthogonal projection      147 180
Orthogonal sequence      132
Orthogonal set      152
Orthonormal basis      168
Orthonormal family      152
Orthonormal sequence      152
Orthonormal set      152
P $\acute{o}$ lya convergence theorem      279
Parallelogram equality      130
Parseval relation      170 175
Partial ordering      210
Partition      618
Perron — Frobenius theorem      469
Picard existence theorem      315
Picard iteration      317
Plane      5
Point of accumulation      21
Point spectrum      371
Polar space      see Dual space
Polarization identity      134
Polynomials      37 250 329 342
Polynomials, Chebyshev      348
Polynomials, Hermite      180
Polynomials, Laguerre      184
Polynomials, Legendre      176
Position operator      575
Positive homogeneous      214
Positive operator      470
Positive part of an operator      497
Positive square root      476
Posterior error bound      302
Power series      548
Power set      612
Pre — Hilbert space      128
Principle of uniform boundedness      246
Prior error bound      302
Product of mappings      616
Product of metric spaces      17
Product of normed spaces      71
Product of operators      528
Product of projections      483
Product of self-adjoint operators      204
Product of sets      612
Product of vector spaces      56
Projection      147 480
Projection operator      147 480
Projection theorem      146
Projection, orthogonal      147 480
Proper extension      616
Proper subset      609
Pseudometrc      46
Pure point spectrum      521
Pythagorean relation      135 152
Quantisation rule      59
quantum mechanics      571
Quantum numbers      588 602
Quotient space      57 71
RANGE      83 101 613
Rare      247
Rational line      29
Rayleigh quotient      469
Real line      5 22 28
Real symmetric matrix      203
Real vector space      51
Rectangular rule      282
Reduction of an operator      491
Reflexive space      241
Regular summabilily method      270
Regular value      371
Relation      618
Relatively compact      406
Representation of functionals      121 188 225
Representation of operators      113
Representative      618
Residual spectrum      171 468 546
Resolvent      370 377 390
Resolvent equation      379
Resolvent kernel      325 456
Resolvent operator      370
Resolvent set      365 371 396
Resonance theorem      255
Restriction of a mapping      615
Restriction of an operator      99
Riemann — Stieltjes integral      226
Riesz lemma      78
Riesz representation in       227
Riesz representation in       188 192
Riesz — Schauder theory      405 436
Right shift operator      201 372 555 562
Rodrigues’ formula      177
Row sum criterion      309
Rydberg constant      606
Scalar field      51
Scalar product      129
Schauder basis      68
Schmidt process      157
Schr $\ddot{o}$ dinger equation      585 598
Schur’s Inequality      393
Schwarz inequality      137 195
Second algebraic dual space      107
Second category      247
Second dual space      239
Segment      65 143
Self-adjoint operator      201 459 534
Semimetric      46
Seminorm      71 195 224
Separable Hilbert space      171
Separable space      21 245
SEQUENCE      25 67 617
Sequence of functionals      266
Sequence of operators      205 408 473
Sequence space      7
Sequentially compact      77 619
Series      67 160
Sesquilinear      130
Sesquilinear form      191
Sesquilinear functional      191
Set      609
shift operators      201 372 555 562
Similar matrices      367
Simpson’s rule      283
Simultaneous corrections      311
Skew — Hemitian matrix      203 368
Space, algebraic dual      106
Space, algebraically reflexive      109 115

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