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/

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Год издания: 1963

Количество страниц: 1084

Добавлена в каталог: 27.02.2015

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Предметный указатель

Convergence of sets, measurable sets in $\Sigma(\mu)$       III.7.1 158
Convergence of sets, properties      III.9.48 174
Convergence of sets, set functions      III.7.2—III.7.4 158—160 IV.8.8 IV.9.4—IV.9.5 IV.9.15 IV.10.6 IV.15
Convergence of sets, set functions, remarks on      389—392
Convergence theorems      IV.15
Convergence theorems for functions of an operator, by inverting sequences      VIII.2.13 650
Convergence theorems for functions of an operator, examples of      VII.8
Convergence theorems for functions of an operator, in finite dimensional spaces      VII.1.9 559 see
Convergence theorems for functions of an operator, in general spaces      VII.3.13 571 VII.3.23 VII.5.32
Convergence theorems for functions of an operator, study of      VII.7
Convergence theorems for kernels      III.12.10—III.12.12 219—222
Convergence theorems for linear operators in F- and B-spaces      II.1.17—II.1.18 54—55 II.3.6 80—82
Convergence theorems, Alexandroff theorem on convergence of measures      IV.9.15 316
Convergence theorems, Arzela theorem on continuous limits      IV.6.11 268
Convergence theorems, Banach theorem for operators into space of measurable functions      IV.11.2—IV.11.3 332—333
Convergence theorems, Egoroff theorem on a.e. and $\mu$ -uniform convergence      III.6.12 149
Convergence theorems, Fatou theorem on limits of integrals      III.6.19 152 III.9.35
Convergence theorems, Lebesgue dominated convergence theorem      III.3.7 124 III.6.16 IV.10.10
Convergence theorems, Moore theorem on interchange of limits      I.7.6 28
Convergence theorems, Vitali theorem for integrals      III.3.6 122 III.6.15 III.9.45 IV.10.9
Convergence theorems, Vitali — Hahn — Saks theorem for measures      III.7.2—III.7.4 158—160
Convergence theorems, Weierstrass theorem on analytic functions      228
Convex combination      V.2.2 414 see "Convex "Convex
Convex function, definition      VI.10.1 520
Convex function, study of      VI.10
Convex hull      V.2.2 414
Convex set      II.4.1 70
Convex set, definition      V.1.1 410
Convex set, study of      V.1—V.2
Convex space, locally      V.2.9 417 471
Convex space, strictly      V.11.7 458
Convex space, uniformly, defined      II.4.27 74
Convex space, uniformly, remarks on      471—474
Convexity theorem of M. Riesz      VI.10.11 525
Convexity theorem of M. Riesz, applications of      VI.11
Convolution of functions as an operator in       XI.3.3 954
Convolution of functions, definition      VIII.1.23 633
Convolution of functions, inequalities concerning      VI.11.6—VI.11.12 528—529
Convolution of functions, properties      VIII.1.24—VIII.1.25 634—635 XI.3.1
Convolution of measures      VIII.2.3 643
Cooke, R.G.      80 926 927
Cooper, J.L.B.      927 932 1258 1273
Correspondence      see "Function"
Coset, definition      35
Countably additive set function      see also "Set function"
Countably additive set function, countable additivity of the integral      III.6.18 152 IV.10.8
Countably additive set function, definition      III.4.1 126
Countably additive set function, extension of      III.5
Countably additive set function, integration with respect to      III.6 IV.10
Countably additive set function, properties      IV.9 IV.15
Countably additive set function, spaces of      III.7 IV.2.16—IV.2.17
Countably additive set function, study of      III.4
Countably additive set function, uniform countable additivity      III.7.2 158 III.7.4 IV.8.8—IV.8.9 IV.9.1
Countably additive set function, weak countable additivity, definition      318
Countably additive set function, weak countable additivity, equivalence with strong      IV.10 318
Covering of a topological space in the sense of Vitali, definition      III.12.2 212
Covering of a topological space in the sense of Vitali, Vitali covering theorem      III.12.3 212
Covering of a topological space, definition      I.5.5 17
Covering of a topological space, Heine — Borel covering theorem      17
Covering of a topological space, Lindeloef covering theorem      12
Cronin, J.      92
Cross product      see "Product"
CS      240
Curve      see "Jordan curve" "Rectifiable
D(I)      1645
da Silvas Dias, C.L.      399
Daniell, P.J.      381—382
Darboux, G.      1588
Davis, H.T.      80
Day, M.M.      82 233 393—394 398 463 729
De Morgan, rules of      2
Decomposition of measures and spaces, Hahn decomposition      III.4.10 129
Decomposition of measures and spaces, Jordan decomposition, for finitely additive set functions      III.1.7 98
Decomposition of measures and spaces, Jordan decomposition, for measures      III.4.7 128 III.4.11
Decomposition of measures and spaces, Lebesgue decomposition      III.4.14 132
Decomposition of measures and spaces, Saks decomposition      IV.9.7 308
Decomposition of measures and spaces, Yosida — Hewitt decomposition      233
Deficiency indices and spaces, definition      XII.4.9 1226
Delsarte, J.      1626
Dense convex sets      V.7.27 437
Dense linear manifolds      V.7.40—V.7.41 438—439
Dense set, definition      I.6.11 21
Dense set, density of continuous functions in TM and       III.9.17 170 IV.8.19
Dense set, density of simple functions in , $1 \le p < \infty$       III.3.8 125
Dense set, nowhere dense set      I.6.11 21
Density of the natural embedding of a B-space $\mathfrak{X}$ into $\mathfrak{X}^{**}$ in the $\mathfrak{X}^{*}$ topology      V.4.5—V.4.6 424—425
Derivative of a set function      III.12.4 212
Derivative of functions      III.12.7—III.12.8 216—217 III.13.3 III.13.6
Derivative of Radon — Nikodym      182
Derivative, chain rule for      III.13.1 222
Derivative, existence of      III.12.6 214
Derivative, properties      IV.15
Derivative, references for differentiation      235
Derivative, space of differentiable functions      IV.2.23 242
Determinant, definition      44—45
Determinant, elementary properties of      I.13
Diagonal process      23
Diameter of a set, definition      I.6.1 19
Diametral point      V.11.14 459
Dieudonne, J.A.      82 84 94 235 387—388 389 391 395 399—400 402 460 462—463 465 466 539 541
Differentiability of the norm, remarks on      471—473 474
Differential calculus      see also "Derivative"
Differential calculus in a B-space      92—93
Differential calculus, Frechet differential      92
Differential equations, solutions of systems of      561 VII.2.19 VII.5.16 VII.5.27
Differential equations, stability of      VII.2.20—VII.2.29 564—565
Differential operator in       XIII.9.E 1549
Differential operator, boundary condition at an end point for      XIII.2.29 1304
Differential operator, boundary condition for      XIII.2.17 1297
Differential operator, boundary form for      XIII.2.1 1287
Differential operator, boundary matrix for      XIII.2.1 1287
Differential operator, boundary value for      XIII.2.17 1297
Differential operator, bounded below      XIII.7.20 1451 XIII.9.C
Differential operator, branching point of      XIII.7.62 1490
Differential operator, characteristic equation of, at infinity      XIII.8 1527
Differential operator, complete set of boundary values for      XIII.2.17 1297
Differential operator, determining set for      XIII.5.22 1374
Differential operator, essential spectrum of      XIII.10.E 1607
Differential operator, finite below $\lambda$       XIII.7.25 1455
Differential operator, first characteristics of      XIII.8 1527
Differential operator, formal      XIII.1.1 1280
Differential operator, formal adjoint of      XIII.2.1 1287
Differential operator, formally positive      XIII.7.6 1439
Differential operator, formally self adjoint      XIII.2.1 1287
Differential operator, Green’s formula for      XIII.2.4 1288
Differential operator, indicial equation of      XIII.8 1504
Differential operator, irregular formal      XIII.1 1280
Differential operator, mixed boundary condition      XIII.2.29 1304
Differential operator, nonselfadjoint      XIII.9.13 1540
Differential operator, real boundary value for      XIII.2.29 1304
Differential operator, regular formal      XIII.1 1280
Differential operator, regular, irregular, singular points for      XIII.8 1504
Differential operator, separated boundary conditions      XIII.2.29 1304
Differential operator, singular boundary value of second order for      XIII.10.D 1604
Differential operator, Stokes lines of      XIII.8 1527
Differential operator, Sturm — Liouville      XIII.2 1291 XIII.9.F
Differentiation theorems      VIII.9.13—VIII.9.14 719—720 see
Dimension of a Hilbert space, as a criterion for Isometric isomorphism      IV.4.16 254
Dimension of a Hilbert space, definition      IV.4.15 254
Dimension of a Hilbert space, invariance of      IV.4.14 253
Dimension of a linear space, definition      36
Dimension of a linear space, invariance of      I.14.2 46
Dimension of a linear space, of a B-space      91—92
Dines, L.L.      466
Dini, U.      360 383 1583
Dirac, P.A.M.      402 1585 1648 1680
Direct product of B-spaces      89—90
Direct sum of B-spaces      89—90
Direct sum of Hilbert spaces      IV.4.17 256
Direct sum of linear manifolds in a linear space      37

Direct sum of linear spaces      37
Directed set, definition      I.7.1 26
Disconnected, extremally      398
Disconnected, totally      41 see
Disjoint family of sets, definition      2
Distinguish between points, definition      IV.6.15 272
Distributions      XIV.3
Distributions, carrier or support of      XIV.3.11 1650
Distributions, definition      XIV.3.2 1645
Ditkin, V.A.      1161
Divisor of zero      IX.1.2—IX.1.7 861
Dixmier, J.      94 398 538 886 935
Dixon, A.C.      1583
Doeblin, W.      730
Domain in complex variables      224
Domain of a function      2
Domain, k-parameter discrete case      VIII.6.9 679
Domain, one-parameter continuous case      VIII.7.7 693
Domain, one-parameter discrete case      VIII.6.8 678
Domain, remarks on      729
Dominated Convergence Theorem      III.3.7 124 III.6.16 IV.10.10
Dominated ergodic theorem, k-parameter continuous case in , $1 < p < \infty$       VIII.7.10 694
Doob, J.L.      729—730 927 929
Dorodnicyn, A.A.      1587
Double norm, definition      XI.6.1 1010
Dowker, Y.N.      723—724 729
Dual group, definition      XI.3.13 968
Dual space (or conjugate space), definition      II.3.7 61
Dubrovskii, V.M.      389
Duffin, R.J.      1265
Dugundji, J.      470
Dunford, N.      82 84 93 232 235 384 387 389 392 462 540—541 543 554 606 609 612 724 727 729—730 927
Dunham, j.l.      1592
Dvoretsky, A.      93
D’Alembert, J.      1582
Eachus, J.J.      1265
Eberlein — Smulian theorem on weak compactness      V.6.1 430
Eberlein — Smulian theorem on weak compactness, remarks on      466
Eberlein, W.F.      88 386 430 463 466 729 927 1273
Edwards, R.E.      381 884
Egoroff theorem on almost everywhere and $\mu$ -uniform convergence      III.6.12 149
Egoroff, D.T.      149
Eidelheit, M.      91 460
Eigenvalue, definition      VII.1.2 556 VII.11 X.3.1
Eigenvector, definition      VII.1.2 556 X.3.1
Eilenberg, S.      385 397
Elconin, V.      92
Ellis, D.      394
Ellis, H.W.      400
Embedding, natural, of a B-space into its second conjugate      II.3.18 66
End point of an interval      III.5.15 140
End point of an interval, fixed      XIII.1 1279
End point of an interval, free      XIII.1 1279
Entire function, definition      231
Entire function, Liouville’s theorem on      231
Equicontinuity and compactness      IV.5.6 260 IV.6.7—IV.6.9
Equicontinuity, definition      IV.6.6 266
Equicontinuity, principle of      II.1.11 52
Equicontinuity, quasi-equicontinuity, and compactness      IV.6.14 269 IV.6.29
Equicontinuity, quasi-equicontinuity, definition      IV.6.13 269 IV.6.28
Equicontinuous family of linear transformations, definition      V.10.7 456
Equicontinuous family of linear transformations, fixed point of      V.10.8 457
Equivalence of normed linear spaces, definition      II.3.17 65
Equivalence, *-equivalence of B*-algebras      IX.3.4 875
Erdoes, P.      384 407
Ergodic theorems      VII.7 VII.8.8—VII.8.10 VIII.4—VIII.8 see "Maximal "Mean "Pointwise "Uniform
Ergodic theorems, remarks on      728—730
Esclangon, E.      1591
Essential least upper bound, definition      III.1.11 100—101
Essential singularity, definition      229
Essential spectrum of a closed operator      XIII.6.1 1393
Essential supremum, definition      III.1.11 100—101
Essentially bounded, definition      III.1.11 100—101
Essentially bounded, E-      X.2 899
Essentially separably valued, definition      III.1.11 100—101
Esser, M.      927
Euclidean space, definition      IV.2.1 238
Euclidean space, further properties      IV.15 374
Euclidean space, study of      IV.3
Euler — Gauss, hypergeometric equation of      XIII.8 1509
Euler, L.      1509 1510 1582
Extended real and complex numbers, definitions      3
Extended real and complex numbers, topology of      11
Extension of a function by continuity      I.6.17 23
Extension of a function, definition      3
Extension of a function, Tietze’s theorem      I.5.3—I.5.4 15—17
Extension of measures to arbitrary sets      III.1.9—III.1.10 99—100
Extension of measures to arbitrary sets, Lebesgue      III.5.17—III.5.18 142—143
Extension of measures to arbitrary sets, to a $\sigma$ -field      III.5
Extensions of linear operators      VI.2.5 478 554
Extremal point and subset, definitions      V.8.1 439
Extremal point and subset, examples and properties      V.11.1—V.11.6 457—458
Extremal point and subset, remarks on      466 473
Extremal point and subset, study of      V.8
Extremally disconnected      398
Ezrohi, I.A.      543
F(S) or $F(S,\Sigma,\mu,\mathfrak{X})$       103
f(T)      557 568 601 1196
F*g      633 951
F-space basic properties      II.1—II.2
F-space basic properties, definition      II.1.10 51
F-space basic properties, examples of      IV.2.27—IV.2.28 243
Factor group, definition      35
Factor sequence      366
Factor space in F- and B- spaces, definition      II.4.13 71
Factor space in F- and B- spaces, properties      II.4.13—II.4.20 71—72
Factor space in F- and B- spaces, remarks on      88
Factor space in vector spaces      38
Fagan, R.E.      406
Fage, M.K.      1587 1589
Fan, K.      395 397 610
Fantappie, L.      399 607
Farnell, A.B.      1163
Fatou theorem on limits and integrals      III.6.19 152 III.9.35
Fatou, P.      152
Fell, J.M.G.      927
Feller, W.      727 1589 1628
Fenchel, W.      471
Feynman, R.P.      406
Fichtenholz, G.      83 233 373 386 388 543
Ficken, F.A.      393 394
Field in algebraic sense      36
Field of subsets of a set, $\sigma$ -field      III.4.2 126 III.5.6
Field of subsets of a set, Borel field      III.5.10 137
Field of subsets of a set, definition      III.1.3 96
Field of subsets of a set, determined by a collection of sets      III.5.6 135
Field of subsets of a set, Lebesgue extension of a $\sigma$ -field      III.5.18 143
Field of subsets of a set, restriction of a set function to      166
Filter, definition and properties      I.7.10—I.7.12 30—31
Finite dimensional function on a group, definition      XI.1.3 940
Finite dimensional spaces, additional properties      IV.15 374
Finite dimensional spaces, definitions      IV.2.1—IV.2.3 238—239
Finite dimensional spaces, study of      IV.3
Finite intersection property, as criterion for compactness      I.5.6 17
Finite intersection property, definition      I.5.5 17
Finite measure (space), $\sigma$ -finite measure      III.5.7 136 see "Measure
Finite measure (space), criterion for and properties      III.4.4—III.4.9 127—129
Finite measure (space), definition      III.4.3 126
Finite measure (space), Saks decomposition of      IV.9.7 308
Finitely additive set function      see also "Set function"
Finitely additive set function, definition      III.1.2 96
Finitely additive set function, study of      III.1—III.3
Fischer, C.A.      380 539 543
Fischer, E.      373
Fixed point property, definition      V.10.1 453
Fixed point property, exercises      V.11.16—V.11.23 459—460
Fixed point property, remarks on      467—470 474
Fixed point property, theorems      V.10
Fleischer, I.      88 400
Foias, C.      1267 1268

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