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| Hille E., Phillips R.S. — Functional Analysis and Semi-Groups |
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| Предметный указатель |
Hartogs, F. 108 760
Hausdorff, F. 609 614
Hausdorff, F., Bernstein — H. — Widder theorem 592
Hausdorff, F., matrices 613
Hausdorff, F., matrices, normalized 614
Hausdorff, F., moment function 614
Hausdorff, F., moment function, algebra 615
Hausdorff, F., moment function, arithmetic 616
Hausdorff, F., moment problem 614
Hausdorff, F., space 3
Hausdorff, F., summability 613
Heisenberg's theory 618
Helly, E. 31
Helly, E., theorems 31 569
Henstock, R. 263
Hermite, C., functions 571
Hermite, C., H. — Weber series (operator) 610 672
Hermite, C., semi-groups 580
Hermite, C., series 571 610
Highberg, I.E. 109
Hilbert, D. 48 92
Hilbert, D., algebra of endomorphisms in H. space 584 705 706 707 718
Hilbert, D., semi-groups in H. space 583
Hilbert, D., space 17
Hilbert, D., transform 605
Hildebrandt, T.H. 32 62 180
Hille, E. 10 83 93 102 103 128 212 221 227 253 265 279 289 291 303 304 310 311 312 324 326 356 362 369 370 377 383 441 453 473 483 488 503 507 538 543 546 552 560 572 580 581 583 605 606 619 621 623 641 642 667 668 669 681 702 714 715 727 756
Hille, E., H. — Yosida theorem 363
Holomorphic, group 278 341 461 494
Holomorphic, semigroup 325 383 472 599
Holomorphic, semigroup, in half-plane 488 669
Holomorphic, solutions to problem C 293
Holomorphic, vector function 92
Homeomorphism 6
Homogeneous, function of degree n (bounded) 110
Homogeneous, operator (real-h.) 24
Homogeneous, polynomial 760
Homogeneous, polynomial, polar form 762
Homogeneous, polynomial, positive-h. functional 29
Homogeneous, polynomial, positive-h. functional, p.-h. and circular 29
Homogeneous, positive-h. subadditive function 252
Homomorphism 9
Homomorphism, kernel of 696
Hopf, E. 503
Hopf, H. 3 740
Hukuhara, M. 237 252
Hurwitz, W.A. 613
Huygens' principle 618
Hyers, D.H. 760
Ideal, (left, right, two-sided, proper, improper) 20 132
Ideal, closure of i. 132 695
Ideal, maximal 132 703
Ideal, maximal, existence of 132 704 705
Ideal, maximal, i. not contained in a m.i. 705
Ideal, nilpotent 700 701
Ideal, primitive 711
Ideal, quotient 697
Ideal, regular 694
Idempotent 121
Idempotent, existence 175
Idempotent, resolvent 174
Image, (inverse i.) 6
Indicator, i.-diagram 481
Indicator, i.-diagram, conjugate i.d. 484 559
Indicator, Phragmen — Lindeloef — Polya i. function 233 480 562
Indicator, semi-group with given i. 485
Infinitesimal generator, classes of i.g.'s 404
Infinitesimal generator, classes of i.g.'s, metric in 410 411
Infinitesimal generator, closely related i. g.'s 409
Infinitesimal generator, conditions on operator to be i. g. 360 363 364 365 369 373 377 380 383 485
Infinitesimal generator, cone of i.g.'s 415 757
Infinitesimal generator, Lie ring of i.g.'s 719
Infinitesimal generator, of adjoint semi-group 426
Infinitesimal generator, of group 364 499
Infinitesimal generator, of group, analytical g. 341
Infinitesimal generator, of group, g. with holomorphic semi-g. extension 500 664
Infinitesimal generator, of group, Lie g. 719
Infinitesimal generator, of perturbed semi-group 389 399
Infinitesimal generator, of semi-group 302 344
Infinitesimal generator, of semi-group, holomorphic s.-g. 483
Infinitesimal generator, of semi-group, Lie s.-g. 750
Infinitesimal generator, operational calculus 434
Infinitesimal generator, relation to infinitesimal operator 344 345 347
Infinitesimal generator, resolvent 337 344
Infinitesimal generator, resolvent, asymptotic expansion 349 488
Infinitesimal generator, resolvent, inversion 349
Infinitesimal generator, resolvent, r. set 457 484
Infinitesimal generator, spectral theory 453
Infinitesimal generator, spectrum 344
Infinitesimal generator, spectrum, example with specified s. 539 551
Infinitesimal operator, domain 307 308 328 329 750 751
Infinitesimal operator, of semi-group of operators 302 306 328 331
Infinitesimal operator, of semi-group of operators, of holomorphic s.-g. 325
Infinitesimal operator, of semi-group of operators, of Lie s.-g. 750
Infinitesimal operator, semi-module of i.o.'s 331
Infinitesimal operator, semi-module of i.o.'s, of i.g.'s 757
Infinitesimal operator, smallest closed extension of i.o. 344
Integral, Bochner 79
Integral, Cauchy 94 166 199 227 441 690
Integral, differentiation of definite i. 88
Integral, Dirichlet 218
Integral, Fejer 221
Integral, Laplace — Stieltjes 213
Integral, Lebesgue 62
Integral, M. Riesz 671
Integral, Pettis 77
Integral, Poisson 227 556 560
Integral, R. — Stieltjes 62
Integral, R. — Stieltjes, in algebra 66
Integral, Riemann — Liouville (fractional integral) 217 663
Integral, singular 89
Interior, finite i. 15
Interior, of set 4
Interior, point 4
Invariant, element (functional) of set of operators 353
Invariant, i. (= normal) subgroup 119 120 683
Invariant, subalgebra 175
Inverse, element (right, left) 20
Inverse, image 6
Inverse, of transformation 6
Inverse, of transformation, linear t. 42
Inverse, quasi-i. element 680
Inversion formulas, F. — Stieltjes t. 570 656
Inversion formulas, Fourier transform 600
Inversion formulas, Laplace (L. — Stieltjes) t. 218
Inversion formulas, Laplace (L. — Stieltjes) t., complex 219
Inversion formulas, Laplace (L. — Stieltjes) t., Phillips 221
Inversion formulas, Laplace (L. — Stieltjes) t., Post — Widder 224
Inversion formulas, resolvent of the infinitesimal generator 339 349 354 382
Irreducible, algebra 175
Irreducible, core (element) of a semi-module 262
Irreducible, representation of algebra 702 712
Isomorphism 9
Jacobi, C.G.J., identities 759
Jacobi, C.G.J., series 611
Jacobson, N. 680 681 682 697 699 702 704 708 710 711
James, R.C. 33
Kakutani, S. 12 32 33 37 38 39 49 50 185 502 503
Kamke, E. 237 252
Kantorovich, L., axioms of K. 303
Kaplansky, I. 680 699 705
Kato, T. 362 641 642 645
Kelley, J.L. 28
Kendall, D.G. 316 534 639
Kernel of algebra 119
Kernel of algebra, of sub-a. 120
Kernel of closed cycle 701
Kernel of homomorphism 696
Kernel of real (complex) linear functional 27
Kernel of singular integral 89
| Kernel, Abel — Hermite 571
Kernel, Fejer 155 221
kernel, Poisson 228
Kernel, smoothing 309 751
Khintchine, A. 654 657
Kitagawa, T. 543
Klee, V.L., Jr. 28 29
Knopp, K., Euler — K. summability 615
Kober, H. 473 664 665
Kolmogoroff, A. 28 634 636 638 639 653
Kolmogoroff, A., Chapman — K. equation 634 648
Kolmogoroff, A., differential equations 638
Kolmogoroff, A., matrix 608 639
Koopman, B.O. 502
Krein, M. 37
Krein, M., K. — Milman theorem 28
Kronecker, L., approximation theorem 146
Kronecker, L., existence theorem 740
Kuratowski, C. 3 765
Laguerre, E.N., polynomial 669
Laguerre, E.N., series (operator) 610
LaSalle, J.P. 28
Lattice 3
Lattice, algebra 151 158 162
Lattice, linear (complete) 16
Laurent's expansion 97
Laurent's expansion for pseudo-resolvent 190
Lax, P. 304 627
Le Roux, J. 618
Lebesgue, H., convergence theorem 83
Lebesgue, H., integral 62 76
Lebesgue, H., translations in L. spaces 535
Ledermann, W. 639
Lee, J.R. 300
Lefschetz, S. 5
Legendre, A.M., series (operator) 611
Lerch's theorem 216
Levy, P. 653 657 673
Levy, P., inversion formula 656
Levy, P., theorem 653
Lie, S. 757 758
Lie, S., group 718
Lie, S., ring 719
Lie, S., semigroup 331 726
Lie, S., theorems 755 757 758
Lie, S., theory 748
Lindeloef, E. 104 229 230 480 609
Lindeloef, E., mu-function 229
Lindeloef, E., P. — L. — Polya indicator 233 480
Lindeloef, E., Phragmen — L. theorem 103 381
Lindenbaum, A. 7
Linear, extension 11
Linear, extension, closed l.e. 13
Linear, functional 26
Linear, functional, bounded 30
Linear, functional, multiplicative 135
Linear, independence (dependence) 11
Linear, multi-l. form 760
Linear, operator 51
Linear, operator,  -adjoint 423
Linear, operator, multiplicative l.o. 303
Linear, space 12
Linear, subspace (manifold) 11
Linear, subspace (manifold), closed l.s. 13
Linear, system 10
Linear, transformation 24 40
Linear, transformation, adjoint 42
Linear, transformation, bounded 41
Linear, transformation, closed 40 45
Linear, transformation, compact 48
Linear, transformation, inverse 42
Liouville, J., Riemann — L. integral 663
Liouville, J., theorem 100
Littlewood, J.E. 239
Locally, analytic (holomorphic) 124 167 200 449
Locally, bounded 112
Locally, bounded, uniformly b. 113
Locally, l. compact space 5
Locally, l. compact space, (B)-space 18
Locally, uniform convergence 777
Logarithm 172 285
Logarithmic, potential 673
Logarithmic, scale 613
Loomis, L.H. 717
Lorch, E.R. 33 109 115 116 121 127 129 164 168 171 173 176 287
Lorch, E.R., (L)-analytic 115 770
Lorentzian distance 674
Lumer, G. 286
Macbeath, A.M. 263
Majorized, infinitesimal generator m. by  435
Majorized, infinitesimal generator m. by , strictly m. 442
Majorized, Lebesgue m. convergence theorem 83
Mapping 6
Markoff, A., algebra 634
Markoff, A., chain (process) 634
Martin, R.S. 109
Maximal, domain of analytic existence 476
Maximal, domain of analytic existence, of semi-group of operators 477 485 538 557 560 599
Maximal, element of partially ordered set 2
Maximal, group 119
Maximal, ideal 132 703
Maximal, ideal, intersection of 133 708
Maximal, ideal, m.i.'s in  147
Maximal, ideal, topology of 137
Maximal, m. principle 3
Maximal, type 104
Mazur, S. 28 36 127 765
Measurability, for operator-valued functions 74
Measurability, for vector-valued functions 72
Measurability, m. implies continuity for semi-groups 280 289 292 303 328 334 743 747
Mehler — Dirichlet integral 612
Meromorphism, domain of 98
Metric, function 7
Metric, space 7
Metric, topology for closed linear transformations 45 198
Metric, topology for closed linear transformations, for infinitesimal generators 410 411
Michal, A.D. 109 760
Milman, D. 33
Milman, D., Krein — M. theorem 28
Mimura, Y. 31
Minimal, element of partially ordered set 2
Minimal, ideal 701
Minimal, rate of growth 496
Minimal, type 104 229
Minkowski, H. 237 252 263
Mittag — Leffler function 668
Miyadera, I. 304 360 365 373 746
Module 262
Modulus, of continuity (rectified) 249
Monodromy, theorem of 98
Moore, E.H. 5
Muentz, H. 98
Multiplicative, linear functional 135
Multiplicative, sub-m. function 141 242
Murray, F.J. 52
Nagumo, M. 120 191 279 284 285
Nathan, D.S. 279 284 285
Neighborhood 3
Neighborhood, basis (n.b. of point) 3
Neumark, M. 131 157 714
Nevanlinna, F. and R. 103
Newton, I., interpolation series 231
Newton, I., interpolation series, i. polynomial 761
Newton, I., potential 673
Nielsen, J. 262
Nilpotent, algebra 688
Nilpotent, element 121
Nilpotent, element, properly q.-n. e. 699
Nilpotent, element, quasi-n. e. 121 128 699
Nilpotent, ideal 700 701
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