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| Kreyszig E. — Introductory functional analysis with applications |
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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 lder inequality 14
Hlder 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  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 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 ![$C[a, b]$](/math_tex/e77e794b3859783600b5f8f2bfed341e82.gif) 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
Schrdinger 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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