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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume III: Analysis |
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| Предметный указатель |
Function, of a-points 225
Function, perturbation of 296
Function, positive definite 304
Function, positive part of 55n
Function, real-analytic 215
Function, real-differentiable 202
Function, reciprocal 23In
Function, regular 207
Function, restrictions on 448
Function, scalar 26
Function, separated 297
Function, set 63 94
Function, sine 41
Function, singularity of 315 319
Function, stem 284
Function, step 54—56 99
Function, upper- (lower-) semicontinuous 463
Function, value of 55n
Function, variance of 107
Function, variation of 454n 456
Function, wave 416
Functional 57
Functional analysis 391
Functional dependence 51
Functional equation 353 367
Functional matrix 45
Functional matrix, rank of 51
Functional, bounded 396
Functional, continuation of 58
Functional, extension of 58
Functional, linear 56 392 393 397
Functional, positive 58
Functional, Riemann extension of 68
Fundamental solution 315 316 317 356
Fundamental theorem of algebra 195—196
Fundamental theorem of Cauchy 10
Fundamental vibration 411
G-set, universal 476
Galois group 510
Galois theory 518
Galois, E. 510
Gamma-function vi 355 365—379 500—501
Gamma-function, Euler functional equation for 367
Gamma-function, Euler integral representation of 371—374
Gamma-function, Stirling formula for 371
Gauss complex plane 255
Gauss distribution 96
Gauss integral theorem 176 181 334
Gauss plane 226 354 355
Gauss plane, line at infinity in 253
Gauss representation, of complex numbers 192
Gauss theorem 430
Gauss — Kronecker integral 429 431—432
Gauss, K.F. 89
Gel'fond, A.O. 517
Gellerstedt problem 335
General solution 292
Geodesic lines 422
Geometry, absolute 508
Geometry, axiomatic method in 507—508
Geometry, Euclidean 507
Geometry, Riemannian 170
Gleason, A. 517
Global behavior, of distributions 81
Global Properties 453
Global uniformizing parameter 250
Global, meaning of 439
Gnedenko, B.W. 121
Goedel 471
Goedel independence theorem 475
Goldbach conjecture 489 490
Goursat, E.J.B. 207
Graded ring 159
Gradient 129
Grassman algebra 159
Grassman algebra, exterior 525
Grassman algebra, of alternating differential forms 154—159
Grassman ring, of differential forms 159
Grassman, H. 124
Green formulas 182 314 316
Green's function 329 410 434
Green's function, existence of 317
Group 313 321 509 519
Group, abelian 521 526
Group, Lie 511
Group, of automorphisms 510 511
Group, topological 4—5 517 518
Group, with operators 511
Group, with parameter 526
Guinea-pig problem 351—352
Hadamard method, of descent 310
Hadamard, J. 313 314 321
Hardy, G.H. 498
Harmonic analysis 518
Harmonic functions 211 318
Hausdorff axioms 264 472
Hausdorff space 2 4 245n 264 266
Hausdorff space, connected 245n
Hausdorff space, connected compact 272
Hausdorff space, example of 6
Hausdorff space, locally Euclidean 262
Hausdorff, separation axiom 4
Heat conduction, equation of 307 319
Heavisfde function H 80 85
Heilbronn 491
Heine — Borel theorem 141 198 233n 256 433 513
Helly, theorem of 105—106
Helmert — Pearson, distribution of 108
Hensel, L. 501 5.19
Hermite theorem 494
Hermite, C. 494
Hesse normal form 192
Hierarchy of structures 521
Hilbert axioms 253 259
Hilbert sequence space 395 397
Hilbert space 393 394 399 400 401 405 412 515 516
Hilbert space, complete 397
Hilbert space, theory of vi
Hilbert's fifth problem 517
Hilbert's seventh problem 494
Hilbert, D. 491 507 508 515 517 523
Hincin 121
Hincin theorem, of continued fractions 499
Hoelder continuous function 337
Hoelder theorem 354 375—379
Hoheisel 487
Holomorphic differential 234
Holomorphic function 207
Holomorphic function in complex plane 215—226
Holomorphic function, differential of 208
Holomorphic function, local derivative 234
Holomorphic function, sequence of 223
Holomorphic part 229
Holomorphy vi
Hopf sigma-process 275
Hull of a set 450
Hurwitz polynomial 300
Hyperbolic (See also Differential equation), motion 194
Hyperbolic Riemann surface 250
Hypercomplex system 525
Hypertranscendental number 493
Ideal 512
Identity Theorem 223 228 247
Incidence theorem 259
inclusion 428 521
Indefinite integral 87n
Indefinite integral of holomorphic function 208
Independence 98—99
Independent Schwartz distribution 82
Indeterminacy, limits of 8—10
| Index set 2
Inertia, index of 322
Infimum (greatest lower bound) 55n
Infinitely divisible distribution 122
Infinitesimal increment 44 45
Infinity, line at 253
Infinity, neighborhoods of 230
Infinity, plane at 273
Infinity, point at 252 253—259 260
Influence, range of 309 311 322
Ingham 486
Initial conditions 292
Initial data, continuous dependence on 308
Initial point 126
Initial value problem 343
Initial values, propagation of 313
Inner composition 514
Inner-mathematical 509
Integrability condition 284
Integrable form 161
integral 53
Integral curve 278 290 291
Integral equation 292 341 514
Integral equation, algebraic 421 435
Integral equation, nonlinear 437—444
Integral equation, of second kind 410
Integral equation, theory of vi
Integral representation 220
Integral representation of functional 64
Integral ring 224
Integral, curvilinear 127 178 235
Integral, definite 57
Integral, step 57
Integral, surface 131 137 179
Integral, volume 179
Integrating factor 285
Integration and measure, theory of 77
Integration, elementary theory of 53—66
Integration, Lebesgue theory of 86
Integration, methods of 277—290
Integration, Stieltjes 65
Interior points 125
interval 54
Inverse, continuity of 7
Isolated 198 449
Isomorphism 92
Isoperimetric problem 422
Iteration 428
Iteration, Picard — Lindelof method 279
Jentzsch theorem 435
Jordan arc 201
Jordan content 62 63 66 76
Jordan curve 200 201
Jordan-measurable 62
Kellogg theorem 339
Kepler, J. 254
Kernel 436
Kernel function 349 438
Kernel matrix 401 403 407
Kernel, oper 64n
kernel, resolvent 440
kinetic energy 416
Kirchhoff law 353
Klein, Felix 507 509
Koenig, H. 86 87
Koksma, J.K. 497
Kolmogorov inequality 114—122
Kolmogorov, A.N. 89 118 121
Krull 511 512
Kurepa 475 485
L-integrable See Lebesgue integrable
L-integral See Lebesgue integral
Lagrange remainder formula 37
Lagrange, J.L. 491
Lame theorem 383
Landau symbol 479 482
Landau, E. 484 487 491
Laplace differential equation 211
Laplace operator 164 177
Laplace transform 346 386—389 404 405
Lattices, structure of 522
Lattices, theory of 512
Laurent series 229 236
Law of Large Numbers, strong 116—119
Law of large numbers, weak 115
Law of large numbers, “empirical” 115
Lebesgue convergence theorem 72
Lebesgue extension, of functional 68
Lebesgue integrability, of functions 87
Lebesgue integrable theorem 73
Lebesgue integral v 53 66 68 101 453
Lebesgue integral, definite 73 87n
Lebesgue measure 53 66
Lebesgue measure zero 60
Lebesgue theory 53
Lebesgue theory of integration 86
Lebesgue theory of measure and integration 508
Lebesgue theory, classical 78
Lebesgue — Stieltjes integral 68 73 78
Lebesgue, H.L. 72 470
Lebesgue-integrable 83 399
Left reciprocal, of matrix 406
Leibniz 23 507
Leonardo of Pisa See Fibonacci
Levi, B. 72
Levy, P. 121
Lewy, H. 313
Liber abbaci 351
Lie groups 511 517
Lie ring 511
Lie, Sophus 517
Limes inferior (lower limit) 8
Limes superior (upper limit) 8
Limit number 196
Limit point 11 196 198
Limit, calculation with 5—6
Limit, concept of 2 3 512
Limit, monotone 58
Limit, theorems of 114—122
Limit, uniqueness of 4
Limits of indeterminacy 8—10
Lindeberg — Feller, theorem of 120
Lindelof conjecture 487
Lindemann — Weierstrass theorem 495
Line at infinity 259 260
Line-element 278 325
Line-element, regular 282
Line-element, singular 282
Linear difference equation 353 354
Linear difference equation, existence theorems for 388
Linear differential equations 286
Linear differential equations of second order 289
Linear form 57
Linear functional 392 393
Linear functional and operators 393
Linear functional, integration of 56
Linear independence, of functions 388
Linear operator 203 392 393
Linear operator, completely continuous 408
Liouville theorem 221 233 492
Liouville, J. 221 296 496
Lipschitz condition 279 281 291 292 425 426
Lipschitz constant 279
Littlewood 498
Ljapunov criterion, for stability 301
Ljapunov Theorem 120 122
Local compactness 453
Local coordinates 185
Local density 453
Local parameter 231 234
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