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Hille E., Phillips R.S. — Functional Analysis and Semi-Groups
Hille E., Phillips R.S. — Functional Analysis and Semi-Groups



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Название: Functional Analysis and Semi-Groups

Авторы: Hille E., Phillips R.S.

Язык: en

Рубрика: Математика/Анализ/Функциональный анализ/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1957

Количество страниц: 808

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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, $(\odot)$-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 $(A_{\infty})$      420
Perturbation theory, for semi-groups of class $(A_{\infty})$, $(1, A)_{u}$      402
Perturbation theory, for semi-groups of class $(A_{\infty})$, $(1, C_{1})$      401
Perturbation theory, for semi-groups of class $(A_{\infty})$, $(C_{0})$      389 400
Perturbation theory, for semi-groups of class $(A_{\infty})$, $H(\Phi_{1}, \Phi_{2})$      417
Perturbation theory, for semi-groups of class $(A_{\infty})$, (1, A)      399
Perturbing operators of class $\mathfrak{T}(A)$      391
Perturbing operators of class $\mathfrak{T}(A), $\mathfrak{B}(A)$      394
Perturbing operators of class $\mathfrak{T}(A), $\mathfrak{T}^{\infty}(A)$      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 $P_{1}$      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 $P_{\nu}$      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 $\mathfrak{X}_{0}$      307
Range, r. space of semi-group $\mathfrak{Y}_{0}$, $\mathfrak{Y}_{0}(x)$      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 $P_{2}$      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 $P_{\nu}$      727 728 741 748 749
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