Dunford N., Schwartz J.T., Bade W.G. — Linear Operators, Part II: Spectral Theory. Self Adjoint Operators in Hilbert Space (Pure and Applied Mathematics: A Series of Texts and Monographs) :: Электронная библиотека попечительского совета мехмата МГУ

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Dunford N., Schwartz J.T., Bade W.G. — Linear Operators, Part II: Spectral Theory. Self Adjoint Operators in Hilbert Space (Pure and Applied Mathematics: A Series of Texts and Monographs)

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Название: Linear Operators, Part II: Spectral Theory. Self Adjoint Operators in Hilbert Space (Pure and Applied Mathematics: A Series of Texts and Monographs)

Авторы: Dunford N., Schwartz J.T., Bade W.G.

Аннотация:

Because oC the large amount of material presented, we have been prevented from including all the topics originally announced for Part II of Linear Operators. The present volume includes all of the material of our earlier announcement associated with the classical spectral theorem for self adjoint operators in Hilbert space. While there are some isolated discussions of nousel fad joint operators, such as that giving the completeness of the generalized eigenfunctions of Hilbert-Schmidt operators in Section ХТ.в, the general theory of spectral operators and the discussion of nonselfadjoint differential boundary value problems have been postponed for inclusion in the forthcoming Part III of this treatise.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1963

Количество страниц: 1084

Добавлена в каталог: 27.02.2015

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Предметный указатель

Spectrum in a finite dimensional space      VII.1.2 556
Spectrum in a general space      VII.3.1 566
Spectrum of a B*-algebra      IX.3.4 875
Spectrum of an element in a B-algebra      IX.1.2 861
Spectrum of an element of a sub B-algebra      IX.1 865
Spectrum of an unbounded operator      599
Spectrum of special bounded operators      VII.5.2—VII.5.15 580—581
Spectrum of special unbounded operators      VII.10.1—VII.10.3 604—605
Spectrum, $\Sigma$ -simple function      X.1 891
Spectrum, continuous      VII.5.1 580 X.3.1
Spectrum, essential, of a closed operator      XIII.6.1 1393
Spectrum, isolated point of      VII.3.15 571
Spectrum, point      VII.5.1 580 X.3.1
Spectrum, residual      VII.5.1 580 X.3.1
Sphere in a metric space      I.6.1 19
Sphere, closed      II.4.1 70
Sphere, closed unit      II.3.1 59
Sreider, Y.      392
Stability of a system of differential equations      VII.2.23 564
Stasevskaya, V.V.      1588 1626
Steinhaus, H.      80—81 94 387—388
Stekloff, W.      1583
Stepanoff, W.      729
Stewart, F.M.      233
Stickelberger, L.      607
Stieltjes moment problem      XII.2 1253
Stieltjes, T.J.      132 142 929 1250 1253 1269
Stokes, G.G.      383 1527
Stone and Banach      see also "Banach — Stone theorem"
Stone space, definition      398
Stone theorems on representation of Boolean rings and algebras      I.12.1 41 44
Stone — Cech compactification theorem      IV.6.22 276 IX.2.16
Stone — Cech compactification theorem, remarks on      385
Stone — Weierstrass theorem      IV.6.16 272
Stone — Weierstrass theorem, complex case      IV.6.17 274
Stone — Weierstrass theorem, remarks on      383—385
Stone, M.H.      41 48 80 85 272 279 382 383—385 393 396 398 442 460 466 606 608 726 872 884 926 927 928 929 1243 1268 1269 1270 1272 1273 1274 1276 1277 1586 1588 1590 1591 1616 1619
Strictly convex B-space, definition      VII.7 458
Strong operator topology, definition      VI.1.2 475
Strong operator topology, properties      VI.9.1—VI.9.5 511 VI.9.11—VI.9.12
Strong topology in a normed space      II.3.1 59 419
Structure space of a B-algebra      IX.2.7 869
Sturm — Liouville operator      XIII.2 1291 XIII.9.F
Sturm, C.      1291 1462 1581 1582 1583
Subadditive function, definition      618
Subbase for a topology      I.4.6 10
Subbase for a topology, criterion for      I.4.8 11
Subspace of a linear space      36 see
Summability of Fourier series      IV.14.34—IV.14.51 361—364
Summability of integrals      IV.13.78—IV.13.101 351—356
Summability of series      II.4.31—II.4.54 74—78
Summability, general principle of      XIII.9.J2 1577
Summability, regular methods      II.4.35 75
Summability, special types of, Abel      II.4.42 76
Summability, special types of, Cesaro      II.4.37 75 II.4.39 IV.14.44
Summability, special types of, Noerlund      II.4.38 75
Summability, special types of, Poisson      IV.14.47 363
Sunouchi, G.      233 234 391 543 552
Sup A      3
Support function, definition      V.1.7 410
Supremum of a set of real numbers      3
Supremum, limit superior of a sequence of sets      126
Supremum, limit superior of a set of real numbers      4
Sylvester, J.J.      606—607
Symmetric difference      41 96
Symmetric operator, definition      X.4.1 906 XII.1.7
Symmetric subspace, definition      XII.4.4 1225
Szasz, O.      384
T(f,s)      668
T*      478 479 879 1188
Tagamlitzki, Y.      396 473
Takahashi, T.      388 400
Taldykin, A.T.      610
Tamarkin, J.D.      80 234—235 388 542 543 610 1118 1162 1269 1274 1276 1583
Tangent function, definition      V.9.2 446
Tangent function, examples      V.11.9—V.11.13 458—459
Tangent function, properties      V.9.1 445 V.9.3 V.11.10—V.11.11
Tangent functionals, definition      V.9.4 447
Tarski fixed-point theorem      I.3.10 8
Tarski, A.      8
Tauber, A.      78 1007
Taylor expansion for analytic functions      228
Taylor, A.E.      92 233 399 540 543 552 554 606 608 612
Taylor, B.      1582
Tchebichef, P.L.      1512
Tchebicheff polynomial      369
Teichmueller, O.      48 927
Thorin, G.O.      541 1183
Tietze extension theorem      I.5.3—I.5.4 15—17
Tietze, H.      15
Tingley, A.J.      406
Titchmarsh — Kodaira theorem      XIII.5.18 1364
Titchmarsh, E.C.      48 612 1160 1364 1586 1587 1590 1591 1592 1614 1616 1618
Titov, N.S.      93
TM(S) or $TM(S,\Sigma,\mu,\mathfrak{X})$       106
Toeplitz, O.      75 79 80 85 399 539 609 926 928 936 1269
Tomita, M.      473
Tonelli theorem      III.11.14 194
Tonelli, L.      194
Topology of real numbers      11
Topology, $\mathfrak{X}$ and $\mathfrak{X}^{**}$ topologies in $\mathfrak{X}^{*}$       419
Topology, base and subbase for      I.4.6 10
Topology, basic definitions      I.4.1 10
Topology, bounded $\mathfrak{X}$ topology      V.5.3 427
Topology, functional or $\Gamma$ topology      V.3.2 419
Topology, functional or $\Gamma$ topology, study of      V.3
Topology, linear spaces      see "Operator topology"
Topology, metric or strong, in a B-space      419
Topology, metric or strong, study of      I.6
Topology, metric, definition      I.6.1 18
Topology, norm or strong, in a normed linear space      II.3.1 59
Topology, product, definition      I.8.1 32
Topology, study of      I.4—I.8
Topology, topological group, definition      II.1.1 49
Topology, topological space, definition      I.4.1 10
Topology, topological space, study of      I.4—I.8
Topology, weak* topology      462
Topology, weak, in a B-space      419
Tornheim, L.      884
Total boundedness in a metric space      I.6.14 22
Total differential      92
Total disconnectedness      41
Total family of functions      II.2.6 58
Total measurability, definition      III.2.10 106 see
Total space of functionals, definition      V.3.1 418
Total variation of a function      III.5.15 140
Total variation of a function, of a set function      III.1.4 97 see
Totally ordered set      I.2.2 4
Tr A      1016
tr(S,T)      1026
Trace of a finite matrix      VI.9.28 515 XI.6.8
Trace of a matrix, definition      VI.9.28 515
Trace of two operators      XI.6.17 1026
Transfinite closure of a manifold      462
Transformation      see also "Operator"
Transformation, measure preserving      667
Transformation, metrically transitive      667
Translate of a function, definition      283
Translation by a vector      36
Translation number      IV.7.2 282
Tseng, Y.Y.      94
Tsuji, M.      388 927
Tukey, J.W.      460—461
Tulajkov, A.      388
Tychonoff theorem on fixed points      V.10.5 456 470
Tychonoff theorem on product spaces      I.8.5 32
Tychonoff, A.      32 372 456 470
Udin, A.I.      396
Ulam, S.      91 1152
Ultrafilter, definition      I.7.10 30

Ultrafilter, properties      I.7.11—I.7.12 30
Unbounded operators in Hilbert space      Chap. XII
Unbounded operators, exercises on      VII.10
Unbounded operators, remarks on      612
Unbounded operators, study of      VII.9
Unconditional convergence of a series      92
Uniform boundedness principle for measures      IV.9.8 309
Uniform boundedness principle in B-spaces      II.3.20—II.3.21 66
Uniform boundedness principle in F-spaces      II.1.11 52
Uniform boundedness principle, discussion of      80—82
Uniform continuity of an almost periodic function      IV.7.4 283
Uniform continuity, criterion for      I.6.18 24
Uniform continuity, definition      I.6.16 23
Uniform continuity, extension of a function      I.6.17 23
Uniform convergence as a criterion for limit interchange      I.7.6 28
Uniform convergence, $\mu$ -uniform convergence, criteria for      III.6.2—III.6.3 145 III.6.12
Uniform convergence, $\mu$ -uniform convergence, definition      III.6.1 145
Uniform convergence, definition      I.7.1 26
Uniform convergence, remarks concerning      382—383
Uniform convexity, definition      II.4.27 74
Uniform convexity, properties      II.4.28—II.4.29 74
Uniform convexity, remarks on      471—474
Uniform countable additivity      see "Countably additive"
Uniform ergodic theory      VIII.8
Uniform ergodic theory, remarks on      730
Uniform operator topology, definition      VI.1.1 475
Uniform operator topology, properties      VI.9.11—VI.9.12 512—513
Unit of a group      34
Unit sphere in a normed space, compactness and finite dimensionality of      IV.3.5 245
Unit sphere in a normed space, definition      II.3.1 59
Unit, adjunction of in a B-algebra      IX.1 860
Unitary equivalence of operators      X.5.12 919
Unitary operator      X.4.1 906
Upper bound for an operator      XII.5.1 1240
Urysohn theorems, for normal spaces      I.5.2 15
Urysohn theorems, metrization      I.6.19 24
Urysohn, P.      15 24
van Dantzig, D.      79 91
van Kampen, E.R.      1160
Variation of a $\mu$ -continuous set function      131
Variation of a countably additive set function      III.4.7 128
Variation of a function      III.5.15 140 see "Total
Variation of a regular set function      III.5.12 137
Variation of a set function      III.1.4—III.1.7 97—98
Variation, semi-variation of a vector-valued measure      IV.10.3 320
Vaught, R.L.      884
Vector space, definition      36
Vector space, dimension of      36
Vector space, elementary properties      I.11
Vector space, real or complex      49
Veress, P.      373 388 392
Vidav, I.      935
Vinkurov, V.G.      94
Vinogradov, A.A.      473
Visser, C.      610 728 933
Vitali theorems on convergence of integrals      III.3.6 122 III.6.15 III.9.45 IV.10.9
Vitali theorems, covering theorem      III.12.2 212
Vitali — Hahn — Saks Theorem      III.7.2—III.7.4 158—160 IV.10.6
Vitali, G.      122 150 158 212 233—234 392
Volterra, V.      79 80 399
von Neumann, J.      80 85 88 235 372 380 386 389 393—394 438 461 538 611 612 659 727 728 884 886 926 927 928 933 934 1145 1152 1163 1240 1257 1263 1268 1269 1270 1272 1273 1274 1585 1588 1591
von Sz.-Nagy, B.      80 373 395 606 608 609 611 612 729 926 927 928 929 931 932 933 935 1259 1262 1263 1265 1270 1272 1273 1274
Vulich, B.Z.      93 396 540 543
Wallach, S.      1587 1592
Wallman, H.      467
Walsh, J.L.      1266 1616 1617
Walters, S.S.      399
Wassilkoff, D.      396
Watson, G.N.      1592
Weak Cauchy sequence, criteria for in special spaces      IV.15
Weak Cauchy sequence, definition      II.3.25 67
Weak completeness of reflexive spaces      II.3.29 69
Weak completeness of special spaces      IV.15
Weak completeness, definition      II.3.25 67
Weak completeness, equivalence of weak and strong convergence in       IV.8.13—IV.8.14 295—296
Weak convergence in special spaces      IV.15
Weak convergence, definition      II.3.25 67
Weak convergence, properties      II.3.26—II.3.27 68
Weak countable additivity and strong      IV.10.1 318
Weak countable additivity, definition      318
Weak limit, definition      II.3.25 67
Weak sequential compactness in reflexive spaces      II.3.28 68
Weak sequential compactness in special spaces      IV.15
Weak sequential compactness, definition      II.3.25 67
Weak topology in a B-space      419
Weak topology, bounded $\mathfrak{X}$ topology in $\mathfrak{X}^{*}$       V.5.3 427
Weak topology, relations with reflexivity      V.4
Weak topology, relations with separability and metrizability      V.5
Weak topology, study of fundamental properties      V.3
Weak topology, weak compactness      V.6
Weak topology, weak operator topology, definition      VI.1.3 476
Weak topology, weak operator topology, properties      VI.9.1—VI.9.12 511—513
Weak topology, weak* topology      462
Weakly compact operator in       VI.8.1 498 VI.8.10—VI.8.14
Weakly compact operator in $L_{\infty}$       VI.9.57 519
Weakly compact operator in C      VI.7.1 490 VI.7.3—VI.7.6
Weakly compact operator, definition      VI.4.1 482
Weakly compact operator, remarks on      539 541
Weakly compact operator, representation of      549
Weakly compact operator, spectral theory of, in certain spaces      VII.4.6 580
Weakly compact operator, study of      VI.4
Wecken, F.J.      927 928 929 933 1269
Wedderburn, J.H.M.      606
Wehausen, J.V.      83 91 381 462 471
Weierstrass, Approximation Theorem      IV.6.16 272
Weierstrass, convergence theorem for analytic functions      228
Weierstrass, K.      228 232 272—273 383—384
Weierstrass, preparation theorem      232
Weil, A.      79 386 1145 1149 1152 1160 1274
Weinberger, H.F.      610
Weinstein, A.      928
Well-ordered set, definition      I.2.8 7
Well-ordered set, well-ordering theorem      I.2.9 7
Wentzel, G.      1614
Wermer, J.      385 930 931 935 1162
Westfall, J.      1583
Weyl — Kodaira theorems      XIII.2.24 1301 XIII.5.13 XIII.5.14
Weyl, H.      372 610 612 725 940 1079 1145 1148 1149 1273 1301 1306 1351 1355 1584 1585 1586 1587 1588 1589 1590 1591
Weyr, E.      607
Whitney, H.      1162
Whittaker, E.T.      1592
Whyburn, G.T.      84
Whyburn, W.M.      1589
Widder, D.V.      383 728 1274
Wiegmann, N.A.      934
Wielandt, H.      934
Wiener closure theorem      see "Closure theorem"
Wiener measure space      405
Wiener theorem on reciprocal of trigonometric series      IX.4.10 881
Wiener — Levy theorem on analytic functions of trigonometric series      IX.4.11 881
Wiener, N.      85 402 405 406 608 728—729 881 978 986 1003 1160 1264
Wilansky, A.      94
Wilder, R.L.      47
Wilkins, J.E., Jr.      936
Williamson, J.H.      609
Windau, W.      1585 1588
Wintner, A.      399 729 926 927 934 1552 1553 1555 1556 1557 1560 1585 1587 1590 1591 1597 1601 1602 1603 1605 1606 1607 1614 1616
Wolf, F.      612
Wolfson, K.      1587
Wright, F.B.      884
Yaglom, A.M.      407
Yamabe, H.      87
Yood, B.      474 610
Yosida      see "Hille — Phillips — Yosida theorem"
Yosida, K.      233 234 373 396 466 539 541 624 715 726 727 728—730 927 929 1587 1628
Young, L.C.      542
Young, W.H.      529
Zaanen, A.C.      80 387 400 609 610 611 936 1277
Zalcwasser, Z.      462
Zermelo theorem on well-ordering      I.2.9 7

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