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| Hille E., Phillips R.S. — Functional Analysis and Semi-Groups |
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| Предметный указатель |
Nilpotent, semi-group 537
Noerlund, N.E. 212 232 234 235 492 494 533
Norm 16
Norm for algebra 22
Norm of Frobenius — Wedderburn 718
Norm, equivalence of n.'s 47 52
Norm, growth of n. of semi-group 306 478 536 552 554 563
Norm, growth of n. of semi-group, convexity of n. 564
Norm, n. (= bound) of functional 30
Norm, n. (= bound) of functional, form 765
Norm, n. (= bound) of functional, polynomial 765
Norm, n. (= bound) of functional, transformation 24
Norm, sub-harmonic function 100
Normal, distribution (Gaussian) 657
Normal, element in (*)-algebra 22
Normal, n. (= invariant) subgroup 119 120 683 699
Normal, operator 584
Normal, operator, semigroup of n.o.'s 593
Normal, topological space 5
Normal, type 104 229
Normal, type, solution to ACP 619
Normed, algebra 22 125 712
Normed, field 127
Normed, group 718
Normed, linear space 17
Normed, semi-group 718
open 3
Open, finitely o. 14
Operation see "Operator"
Operational calculus, for closed linear operators 199
Operational calculus, for infinitesimal generators 434
Operational calculus, for infinitesimal generators, amended 442
Operational calculus, for infinitesimal generators, analytical dependence 446
Operational calculus, in (B)-algebra with unit 164
Operational calculus, in (B)-algebra with unit, without u. 689
Operational calculus, in commutative (W*)-algebra (extended o.c.) 586
Operator (= endomorphism — operation), adjoint 42 161
Operator (= endomorphism — operation), adjoint,  -a. 423
Operator (= endomorphism — operation), adjoint, self-a. 161 584
Operator (= endomorphism — operation), bounded linear o.'s (endomorph-isms) 51
Operator (= endomorphism — operation), closed linear o.'s 55
Operator (= endomorphism — operation), closed linear o.'s, spectral theory for c.l.o. with compact resolvent 210
Operator (= endomorphism — operation), commutant of an o. 424
Operator (= endomorphism — operation), compact linear o. 48
Operator (= endomorphism — operation), compact linear o., spectral theory 180
Operator (= endomorphism — operation), contraction 353
Operator (= endomorphism — operation), infinitesimal o. 306
Operator (= endomorphism — operation), infinitesimal o., set of 331
Operator (= endomorphism — operation), normal 584
Operator (= endomorphism — operation), perturbing 394
Operator (= endomorphism — operation), positive 353
Operator (= endomorphism — operation), projection 52 163 584
Operator (= endomorphism — operation), resolvent 54
Operator (= endomorphism — operation), transition 353
Operator (= endomorphism — operation), unitary 584
Order of determining function 214
Order of entire function 104
Order of holomorphic function in half-plane 229
Order of holomorphic function in half-plane, in sector (subexponential o.) 490
Order of holomorphic function in half-plane, on vertical lines 229
Order on circle 489
Oriented envelope of closed set with respect to a function 166 199
Oriented envelope of spectral set 177
Orlicz, W. 61 109 573 765
Oscillating, slowly (feebly) 505 508
Osgood, W.F., theorem 113 114
Parameter, parametric, semi-group 258 727
Partial ordering 2
Partial ordering for bounded self-adjoint operators 162
Partial ordering in (A*)-algebras 151
Partial ordering in (B*)-a.'s 158
Partial ordering in (C*)-a.'s 162
Partial ordering in linear systems 15
Partial ordering in linear systems, semi-groups on a p.o.l.s. 303 353
Peck, J.E.L. 738
Perlis, S. 680 699
Permanency, law of 98
Perturbation theory, for semi-groups of class  420
Perturbation theory, for semi-groups of class ,  402
Perturbation theory, for semi-groups of class ,  401
Perturbation theory, for semi-groups of class ,  389 400
Perturbation theory, for semi-groups of class ,  417
Perturbation theory, for semi-groups of class , (1, A) 399
Perturbing operators of class  391
Perturbing operators of class  \mathfrak{B}(A)$ 394
Perturbing operators of class \mathfrak{T}^{\infty}(A)$ 392
Perturbing operators, A-extension 392
Perturbing operators, bounded 389
Pettis, B.J. 33 38 61 62 72
Pettis, B.J., integral 77
Phillips, R.S. 37 40 49 50 62 77 89 129 141 155 210 221 223 242 304 305 306 310 321 344 360 365 372 373 377 402 417 422 446 453 463 483 503 580 583 598 606 612 619 621 622 623 660 663 674 739
Phragmen, E. 480
Phragmen, E., P. — Lindeloef theorem 103 381
Phragmen, E., P. — Lindeloef — Polya indicator 233 480
Picard, E. 617
Pierpont, J. 531
Pincherle, S. 492
Pitt, H.R. 149 505
Plancherel theorem 599
Plessner, A. 534
Poincare, H., asymptotic in the sense of P. 349 357 487 488
Point spectrum 54
Point spectrum of Abel summability semi-group 608
Point spectrum of translation semi-group 532 533
Point spectrum of trigonometric semi-group 549
Point spectrum, contains poles of resolvent 194
Point spectrum, contains poles of resolvent, characterization of p. of r. 521 522 668
Point spectrum, ergodic properties of p.s. 518 525
Point spectrum, index 55
Point spectrum, mapping of p.s. 204 464 465
Point spectrum, property  54
Point spectrum, relation between p.s. of semi-group operators and generator 467 470
Poisson, S.D., distribution 314 636 650 657
Poisson, S.D., integral 556 560
Poisson, S.D., kernel 228 658
Poisson, S.D., summability 543 556
Poisson, S.D., transform 579 604
Pollard, H. 14
Polya, G., Phragmen — Lindeloef — P. indicator 480
Polynomials, abstract (homogeneous) 760
Polynomials, Newton's interpolation p. 761
Polynomials, orthogonal p., Hermite 610
Polynomials, orthogonal p., Laguerre 610 669
Polynomials, orthogonal p., Legendre 611).
Positive, cone 15
Positive, cone, open, finitely open 289
Positive, element 15
Post, E.L. 224 435 670
Post, E.L., P. — Widder inversion formula 224 362
Postulates see "Axioms and Conditions"
Power 174
Power, (F)-p., (G)-p. 768
Power, abstract p. series 109
Power, abstract p. series, (F)-p. s. 775
Power, abstract p. series, (G)-p. s. 770
Power, p. group 174
Power, p. group, continuous 285
Power, p. semigroup 539
Price, G.B. 62
Principle of analytic continuation 98
Principle of indeterminancy 618
Principle of scientific determinism 618
Principle of the maximum 99 114
Principle of uniform boundedness 26
Principle, correspondence 168 337 689
Principle, Huygen's 618
Principle, maximal 3
Probability matrices 633 634
Problem, A 278 280
Problem, A, strong case 303
| Problem, B 278 288
Problem, B, strong case 327
Problem, C 279 291
Problem, correctly (= well) set p. 357 617
Problem, D 279 300
Product, Cartesian p. (p. space) 5
Product, cross p. 681
Product, defined by convolution 141 615 649 701
Product, inner p. 17
Product, p. system, algebra 20
Product, p. system, linear 12 19
Product, restricted p. 268
Product, ring p. 19
Product, scalar p. 11
Projection operator 52
Projection operator in Hilbert space 163 584
Projection operator, ergodic 514
Property  54
Pseudo-, norm 137
Pseudo-, resolvent 126 183
Putnam, A. 703
Quasi-, inverse 680
Quasi-, nilpotent element 121 128 699
Quasi-, nilpotent element, properly q.-n. e. 699
Quasi-, nilpotent element, semi-group of q.-n. e.'s 481
Quasi-, radical 699
Quasi-, regular 680
Quasi-, resolvent 175
Quotient, algebra 133 696
Quotient, q. of ideal relative to algebra (q. ideal) 697
Quotient, space 18
Radical 133 699
Radical algebra 701
Radical as intersection of ideals 133 708
Radical, algebra without r. (semi-simple a.) 133 699
Radical, nilpotency of r. 701
Radical, quasi-r. 699
Radical, Segal r. 708
Radical, weak r. 710
Raikov, D.A. 139 155
Range, of adjoint to l.t. 44 45
Range, of linear t. 40 44
Range, of linear t., r. of second category 46
Range, of transformation 5
Range, r. space of semi-group  307
Range, r. space of semi-group  ,  328
Realization, of semi-group 258
Rectifiable arc, in (B)-algebra 66
Reducible, algebra 175
Reducible, element of semi-module (indefinitely r. s.-m.) 262
Regular, (B)-space (= reflexive) 33
Regular, element 20 118
Regular, element, quasi-r. e. 680
Regular, element, semi-r. e. 702
Regular, element, set of r.e.'s (= maximal group) 119
Regular, ideal 694
Regular, ideal, maximal r. i. 704
Regular, space 5
Rellich, F. 50
Representation, by binomial series 234
Representation, by binomial series, of semi-groups 489
Representation, by Laplace integrals 230
Representation, by Laplace integrals, of resolvent of infinitesimal generator 338 344 486
Representation, Dirichlet r. of Fourier semigroups 547 576
Representation, of (A*)-algebras 151
Representation, of (B)-algebras 136 711 712
Representation, of (B)-algebras, irreducible r. 702 712
Representation, of (B)-algebras, sufficiency of r. 714
Representation, of (B*)-algebras 157
Representation, of groups 715 716
Representation, of semigroups 258 455 715
Residual spectrum 54
Residual spectrum of power semi-group 539
Residual spectrum, ergodic implications of r.s. 520
Residual spectrum, mapping of r.s. 204 464 465
Residual spectrum, property  54
Residual spectrum, relation between r.s. of operator and point spectrum of its adjoint 56 426
Residual spectrum, relation between r.s. of semi-group operators and generator 469 471
Residue class, algebra 133 696
Residue class, linear system 18
Residue class, norm 18 134
Resolution, of the identity 160 163 585 587 601 603 604
Resolution, spectral r. of element 177 688
Resolution, spectral r. of operator 207
Resolvent, analytic extension 126 185 189
Resolvent, equations, first 126 183
Resolvent, equations, second 126 195
Resolvent, is holomorphic 123 184
Resolvent, is holomorphic, at infinity 190
Resolvent, is holomorphic, entire 190 195 484 537 664 668 676
Resolvent, Laurent expansion 190
Resolvent, poles of r. 194 521 522 524
Resolvent, pseudo-r. 126 183
Resolvent, quasi-r. 175
Resolvent, r. of element 123
Resolvent, r. of element, of linear operator 54
Resolvent, r. of semi-group generator 337
Resolvent, r. of semi-group generator, inversion of r. 339 349
Resolvent, r. set 54 123
Resolvent, representation of r. 186
Resolvent, singular at infinity 193
Reuter, G.E.H. 639
Reverse, reversible, r. group 681
Rickart, C.E. 62 120 129 130 289
Riemann, B., R. function 617
Riemann, B., R. — Liouville integrals 663
Riemann, B., R. — Stieltjes integrals 62
Riesz, F. 31 35 37 92 162 174 180 502
Riesz, M. 313 316 545 573 606 672 673 674 675 676 677
Riesz, M., inequality 313
Riesz, M., integrals 671
Riesz, M., operator (potential) 673 674 677
Ring 9 681
Ring, Lie r. 331
Ring, r. multiplication 19
Romanoff, N.P. 435 610
Rosenbaum, R.A. 237 240 253
Runge theorem 170 201 692
Scalar, field 11
Scalar, multiplication 11 20
Schaeffer, J.J. 286
Schauder, J. 49 180
Scheffers, G. 757 758
Schmidt, R. 505
Schur, I. 37 256 718 719
Schwartz, J. 50 509
Schwartz, L. 319 446
Schwarz, H.A., inequality 17
Schwarz, H.A., lemma 100
Scientific determinism, principle of 618
Scorza-Dragoni, G. 740
Segal, I.E. 155 312 336 534 680 695 699 704 705 708
Self-adjoint, algebra 161
Self-adjoint, element 22
Self-adjoint, operator 161 584
Self-adjoint, operator, semi-group of s.-a.o.'s 587
Semi-group, abelian 257
Semi-group, abstract 256
Semi-group, abstract, realization 258
Semi-group, additive (= semi-module) 257
Semi-group, adjoint 426
Semi-group, algebra associated with s.-g. 455 715
Semi-group, continuity at the origin 317 321
Semi-group, Hermitian 580
Semi-group, holomorphic 472
Semi-group, holomorphic, in half-plane 488 669
Semi-group, holomorphic, structure 478
Semi-group, hyperbolic 271
Semi-group, Lie 726 748
Semi-group, Lie, assumptions 727 728 741 748 749
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