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| Hille E., Phillips R.S. — Functional Analysis and Semi-Groups |
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| Предметный указатель |
Abel, N.H., A. — Hermite kernel 571
Abel, N.H., average 504
Abel, N.H., ergodic 511
Abel, N.H., limit 504
Abel, N.H., summability 321 543 556 581 607
Abelian, algebra 20
Abelian, group 10
Abelian, semi-group 257
Abelian, theorems 503
Abscissas of convergence, binomial series 232
Abscissas of convergence, Laplace — Stieltjes transform 215
Abstract, Cauchy problem 617
Abstract, Cauchy problem, of order n 623
Abstract, integration 58
Abstract, polynomial 760
Abstract, semigroup 256
Abstract, space 2
Addition theorem for exponential function 122 172 278 282
Addition theorem, in (B)-algebra 277
Additive, group 9
Additive, group, g. space 10
Additive, resultant 262
Additive, set function 75
Additive, spaces 9
Additive, transformation 23
Adjoint,  -a. operator 422 423
Adjoint, -a. space 422 429
Adjoint, element of an algebra 22
Adjoint, semigroup 426
Adjoint, space 32
Adjoint, theory 421
Adjoint, transformation 42
Adjoint, transformation, second a.t. 43
Alaoglu, L. 37 303 502
Alexandroff, P. 3 740
Alexiewicz, A. 109
Algebra 19
Algebra of endomorphisms 51 702
Algebra of Hausdorff matrices 615
Algebra with unit element 20 117
Algebra without u. e. 680
Algebra, a. associated with semi-group 455
Algebra, Banach 21
Algebra, commutative 20
Algebra, difference (= quotient = residue class) 133 696
Algebra, Markoff 634
Algebra, nilpotent 688
Algebra, primitive 711
Algebra, radical of a. 133 699
Algebra, reducible (irreducible) 175
Algebra, self-adjoint a. 161
Algebra, semi-group a. 715
Algebra, semi-simple 133 699
Algebra, semi-simple, weakly 708
Algebra, simple 714
Algebra, star 22
Algebra, star, (A*)-a. 22
Algebra, star, (B*)-a. 22
Algebra, star, (C*)-a. 161
Algebra, star, (W*)-a. 161 584
Algebra, sub-a. 20
Algebra, sub-a., invariant 175
Algebra, sub-a., least s.-a. 20
Algebra, topological a. 21
Algebra, topological a., normed 22
Algebra, two-sided 704
Algebra, zero a. 694
Algebraic, space 19
Algebraic, system 9
Analytic, continuation 98 113
Analytic, continuation, of semigroups 473 675
Analytic, dependence in the operational calculus 164 168 200 446 690
Analytic, function 98
Analytic, function, Frechet 112 778
Analytic, function, Lorch 115
Analytical, group 278 341
Analytical, semi-group 472
Andersen, A.F. 507
Angular semi-module 252 265
Approximation of the identity 325 555 579 582
Approximation, Bernstein's a. theorem 317 534
Approximation, Kronecker's a. theorem 146
Approximation, Stone — Weierstrass a. theorem 151
Approximation, Weierstrass a. theorem 534
Arens, R.F. 131 140
Arithmetic of distribution functions 657
Arithmetic of moment functions 616
Assumptions,  on topological semi-group 727 728 741 748 749
Assumptions,  on parameter semi-group 741 742
Austin, D.G. 638
Automorphism 9
Axiom of Choice 3
Axiom, countability 4
Axiom, Kantorovich 303
Axiom, Lindenbaum 7
Axiom, Separation 4
Axiom, triangle 7
Baer, R. 699
Baire, R., B. continuity 765
Baire, R., condition of B. 271
Baker, B.B. 618 675
Baker, G.A., Jr. 271
Balakrishnan, A.V. 446 580 674
Banach, S. 17 28 29 32 37 39 40 41 44 46 47 109 180 546
Banach, S., algebra 21
Banach, S., B. — Steinhaus theorem 41
Banach, S., Hahn — B. extension theorem 28
Banach, S., lattice 636
Banach, S., limit functional 39
Banach, S., space 16
Basis, of a linear system 11
Begle, E.G. 14 263
Bergstroem, V. 262
Bernstein, F. 617
Bernstein, S., approximation theorem 317 534
Bernstein, S., B. — Hausdorff — Widder theorem 592 612
Bessel, F.W., function 222
Beurling, A. 141 243 245
Binomial, distribution 316
Binomial, series 231 489 669
Binomial, series, convergence 232
Binomial, series, representation 234
Birkhoff, G. 16 62 303 502 636 727
Birkhoff, G.D. 502
Bochner, S. 62 67 76 129 155 230 570 592 673 674
Bochner, S., integral 78
Bohnenblust, F. 29 30 214 473
Borel, E., property 4
Borel, E., sets 141 158
Borel, E., transform 340
Bound see "Norm"
Bound, lower 2
Bound, lower, greatest l. 3
Bound, upper 2
Bound, upper, least u. 3
Boundary 4
Boundary value problems, for partial differential equations 617
Boundary value problems, for semi-groups 498
Bounded, homogeneous function 110
Bounded, set 8
Bounded, set, totally b.s. 8
Bounded, transformation 24
Bounded, variation (strong, weak) 59
Boundedness of norm of semi-group 280 304 746
Boundedness of subadditive function 241 253
Boundedness of suboperative function 742
Boundedness, uniform b. principle (theorem) 26
Bourbaki, N. 37
Brunn — Minkowski — Lusternik, inequality 263
Burgess, D.C.J. 71
| Butzer, P.L. 326
c-star set 109
Calkin, J.W. 705 706
Cancellation, law of 10 257
Canonical, function 728
Canonical, one-parameter c. semi-group 259
Canonical, one-parameter c. semi-group, sub-s.-g. 728
Canonical, orbit 728 735
Canonical, orbit, hyperbolic case 274
Carleman, T. 502
Carlson, F. 103 212 233 492 496
Cartan, E. 718
Category, first (second) 4
Category, Zorn's c. theorem 271
Caton, W.B. 221
Cauchy, A., abstract C. problem 617
Cauchy, A., abstract C. problem, of order n 623
Cauchy, A., C. — Hadamard theorem 96
Cauchy, A., condition 8
Cauchy, A., estimates 97 111
Cauchy, A., integrals 94 111 166 199 227 441 690
Cauchy, A., problem 617 674
Cauchy, A., sequence 8
Cauchy, A., theorem 95
Cesaro, E., average 504
Cesaro, E., ergodic 511
Cesaro, E., limit 504
Cesaro, E., summability 321 613 616
Chapman — Kolmogoroff, equation 634 648
CHARACTER 716
Character of real line 145
Character of real line, c. group 600
Characteristic, function 653
Characteristic, function, unilateral 660
Characteristic, manifold (value, vector) 54
Circular, set 12
Clarkson, J.A. 19
Classes of semi-groups,  ,  428
Classes of semi-groups,  ,  ,  , (1, A), (0, A), (A) 320
Classes of semi-groups,  325
Classes of semi-groups, (E) 509
Classes of semi-groups, primed c. 323
Clopen (= closed and open) 4
Closed, boundedly weakly* c. 39
Closed, c. graph theorem 47
Closed, linear operators, class of 55
Closed, linear operators, operational calculus 199
Closed, linear operators, powers 56
Closed, linear operators, resolvent theory 183
Closed, linear operators, spectral theory 203 207 210)
Closed, regularly c. 39
Closed, set 3
Closed, transformation 40
Closed, transformation, class of c. linear t. 45
Closely related, infinitesimal generators 409 446
Closely related, linear transformations 45
Closely related, linear transformations, l. operators 198
Closure 3
Closure, relative 4
Cohen, L.W. 502
Commutant, of a set 21
Commutant, of commutant 453
Commutator 722 758
Compact 5
Compact, Borel property 4
Compact, conditionally c. 5
Compact, linear operator 52
Compact, linear operator, spectral theory 180
Compact, locally c. space 5
Compact, resolvent (spectral theory) 210
Compact, sequentially c. 8
Compact, sequentially c., weakly 35
Compact, transformation (weakly) 8 48
Compact, weakly c. 48
Components, of maximal group 119
Components, of maximal group, number of c. 287
Components, of maximal group, principal c. 119
Components, of resolvent set (principal c.) 124
Components, of reversible group (principal c.) 683
Components, of set 4
Conditions,  321
Conditions,  322
Conditions,  323
Conditions,  ,  322
Conditions, (A)'' 323
Conditions, (A), (A)' 322
Conditions, (W) 141 435
Cone, in  252
Cone, in (B)-space 289
Cone, of generators 658
Cone, positive c. of partially ordered linear system 15
Cone, retrograde light c. 675
Conjugate, of derivative 556 579
Conjugate, operator 605
Conjugate, space 32
Connected 4
Continuity, absolute 76
Continuity, in the sense of Baire 765
Continuity, modulus of c. (rectified) 249
Continuity, of additive transformations 23
Continuity, of additive transformations, bounded 24
Continuity, of homogeneous polynomials 764
Continuity, of linear forms 764
Continuity, of subadditive functions 246
Continuity, of subadditive functions, in the mean 249
Continuity, strong 58 59
Continuity, uniform 59
Continuity, upper semi-c. 167
Continuity, weak 58 59
Continuous spectrum 54
Continuous spectrum of semi-group of Riemann — Liouville integrals 668
Continuous spectrum of semi-group of Riemann — Liouville integrals, group extension 665
Continuous spectrum of translation semi-group 532 533
Continuous spectrum, mapping of 204 464 465
Continuous spectrum, property  54
Continuous spectrum, relation c.s. of semi-group operators and generator 469 471 665
Convergence in measure 72
Convergence in variation 649
Convergence of (F)-power series 775
Convergence of (F)-power series, (G)-p.s. 770
Convergence of binomial series 232
Convergence of directed set 5
Convergence of directed set, weak 35
Convergence of Laplace — Stieltjes transform 213
Convergence, absolute 60
Convergence, almost everywhere 72
Convergence, almost uniformly 71
Convergence, c. preserving transformation 607 609
Convergence, locally uniform 169 200 777
Convergence, strong 60
Convergence, theorem of P. Levy 653
Convergence, unconditional 61
Convergence, uniform 61
Convergence, weak 60
Convex, c-convex 774
Convex, c. extension 12
Convex, c. extension, closed 13
Convex, extreme points of c. set 28
Convex, extreme points of c. set, ordinary, exceptional 483
Convex, function 239
Convex, semi-module 560
Convex, set 11
Convex, set, additive resultant of 263
Convex, set, function of support for 252
Convex, uniformly c. 19
Convolution algebra 141 153 615 649 701
Cooper, J.L.B. 583
Cooper, R. 243
Copson, E.T. 618 675
Courant, R. 48
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