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

$(S,\Sigma,\mu)$       126
$(\partial_v(\Sigma))^j$       1699
      522
$A(\alpha)$       685
      1280
$A^{(k)}(I)$       1652
      619
$A_{\pi}^{(k)}(I)$       1662 1663
$B(S,\Sigma)$       240
$B(\mathfrak{X},\mathfrak{Y})$       61
$ba(S,\Sigma)$       240
$ba(S,\Sigma, \mathfrak{X})$       160
      239
$ca(S,\Sigma)$       240
$ca(S,\Sigma,\mathfrak{X})$       161
      242 1638
$C^{\infty}(I)$       1638
      239
      1638
$C_0^{\infty}(I)$       1638
      1089
$C_{\pi,0}^{\infty}(I)$       1660
$C_{\pi}^p(C)$       1660
$C_{\pi}^{\infty}(C)$       1660
$D \pi (I)$       1660
$e(\lambda)$       558
$E(\sigma)=E(\sigma;T)$       573
$E(|f| > \alpha)$       101
      238
      1684
$F(\alpha,\beta;\gamma;z)$       1509
      1668
      1287
$F_t^{l}j(\tau)$       1287
$F_{\pi}(C)$       1660
      1649
      1287
$H^{(k)}(I)$       1652
      1291
$H_0^{(k)}(I)$       1652
      35
$H_{\pi,0}^{(k)}(I)$       1662
$H_{\pi}^{(k)}(I)$       1662 1663
$H_{\tau}^n(I)$       1287
      239
as a B-algebra      XI.3.2 953
      239
$L_p(S,\Sigma,\mu)$       241
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , characterizations of      394—396
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , completeness of      III.6.6 146 III.9.10
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , criteria for convergence in      III.3.6—III.3.7 122—124 III.6.15 IV.15
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , definition      III.3.4 121
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , remarks on      387—388
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , separable manifolds in      III.8.5 168 III.9.6
$L_p(S,\Sigma,\mu)$ , $1 \le p < \infty$ , study of      III.3 III.6 IV.8 IV.15
$L_p(S,\Sigma,\mu)$ , 0<p<1, definition      III.9.29 171
$L_p(S,\Sigma,\mu)$ , 0<p<1, properties      III.9.29—III.9.31 171
$L_p(S,\Sigma,\mu,\mathfrak{X})$       121
$L_p^0(S,\Sigma,\mu,\mathfrak{X})$       119
      238
$L_{\infty}$       239
$L_{\infty}(S,\Sigma,\mu)$       241
$L_{\infty}(S,\Sigma,\mu)$ , definition      IV.2.19 241
$L_{\infty}(S,\Sigma,\mu)$ , study of      IV.8 IV.15
$N(M_0;\epsilon,A)$       869
,       1227
or $P_{x \in X} A_x$       9
      9
$P_{\infty}$       955
$R(\lambda;T)$       566
$rba(S,\Sigma,\mathfrak{X})$       161
$rca(S,\Sigma,\mathfrak{X})$       161
$S(A,\epsilon)$       19
$S(x,\epsilon)$       19
$TM(S,\Sigma,\mu)$       243
$T_0(\tau)$       1291 1679
$T_1(\tau)$       1291 1679
$v(\mu)$ or $v(\mu,E)$       97
$x(\mathfrak{M})$       868
$x^{**}$ , $\mathfrak{X}^{**}$       66
$x^{*}$ , $\mathfrak{X}^{*}$       61 860
$\alpha * \beta$       643
$\bar{\tau}$       1639
$\bigcirc$       1669
$\bigtriangledown^2$       1631
$\bigtriangleup$       96
$\chi_E$       3
$\epsilon$       1
$\frac{d \lambda}{d \mu}$       182
$\hat{x}$ , $\hat{X}$       66
$\hat{\mu}$       134
$\lim \inf_{n \to \infty} a_n$       4
$\lim \inf_{n \to \infty} E_n$       126
$\lim \inf_{x \to 0} f(x)$       4
$\lim \inf_{x \to 0} ^{+} f(x)$       4
$\lim \sup_{n \to \infty} a_n$       4
$\lim \sup_{n \to \infty} E_n$       126
$\lim \sup_{x \to 0} f(x)$       4
$\lim \sup_{x \to 0} ^{+} f(x)$       4
$\lim_{f(a) \to x} g(a)$       26
$\lim_{n \to \infty} E_n$       126
$\mathcal{P} \integral$       1050
$\mathcal{P}(A)$       630
$\mathcal{R}(z)$       4
$\mathfrak{A}$       955
$\mathfrak{B}$       895
$\mathfrak{D}(T)$       1185
$\mathfrak{D}(T^n)$       602
$\mathfrak{D}(T^{\infty})$       602
$\mathfrak{D}_+$ , $\mathfrak{D}_-$       1226
$\mathfrak{F}(T)$       557 568 600
$\mathfrak{H}$       242
$\mathfrak{I}(z)$       4
$\mathfrak{K}$       410
$\mathfrak{L}(A)$       642
$\mathfrak{M}$       868
$\mathfrak{N}_{\lambda}^n$       556
$\mathfrak{R}(T)$       1185
$\mathfrak{S}^{*}$       1230
$\mathfrak{V}(A)$       642
$\mathfrak{X} / \mathfrak{M}$       38
$\mathfrak{X}^{+}$       418
$\mu^{*}$       99
$\mu^{+}$ , $\mu^{-}$       98 130
$\nu(\lambda)$       556
$\Omega(x)$       1052
$\omega_0$       619
$\ominus$       249
$\oplus$       37 256
$\overline{A}$       11
$\overline{co}(A)$       414
$\overline{sp}(B)$       50
$\overline{T}$       1226
$\partial^J$       1636
$\perp$       72 249
$\Phi$       1
$\rho(T)$       566
$\rho(x)$       861
$\rho(x,y)$       18
$\sigma(T)$       556 566
$\sigma(x)$       861
$\sigma(\mathfrak{X})$       875
$\Sigma(\mu)$       156
$\sigma_c(T)$       580
$\sigma_e(T)$       1393
$\sigma_e(\tau)$       1393
$\sigma_p(T)$       580
$\sigma_r(T)$       580
$\tau$       446 963
$\tau^{*}$       1639

$\tau^{+}$       1639
$\tilde{f}$       951
$\vee$       888
$\wedge$       888
$\xi^{J}$       1635
$\| F \|_{k}$       1663
$\| T \|$       1010
$\| \mu \|$       320
$^{*}_{=}$       875
$^{\rightarrow}_{\rightarrow}$       1645 1660
      1089
$|T|_{\infty}$       1089
'      2
((S,T))      1013
(a,b], etc.      4
(x,y)      242
(x,y)*      1224
a(a)      522
A(d)      242
A(n)      661
A(T,n)      661
a.e.      see "Almost everywhere"
Abdelhay, J.      397
Abel summability of series      II.4.42 76
Abel, N.H.      76 352 383
Abelian group      34
Absolute convergence, in a B-space      93
Absolutely continuous functions, definition      IV.2.22 242
Absolutely continuous functions, set function      see "Continuous set function" "Set
Absolutely continuous functions, space of, additional properties      IV.15 378
Absolutely continuous functions, space of, definition      IV.2.22 242
Absolutely continuous functions, space of, remarks concerning      392
Absolutely continuous functions, space of, study of      IV.12.3 338
AC(I)      242
Accumulation, point of      I.4.1 10
Adams, C.R.      393
Additive set function      see "Set function"
Adjoint element in an algebra with involution      40 see
Adjoint of an operator between B-spaces      VI.2
Adjoint of an operator in Hilbert space      VI.2.9 479 VI.2.10
Adjoint of an operator, compact operator      VI.5.2 485 VI.5.6 VII.4.2
Adjoint of an operator, continuity of operation      VI.9.12 513
Adjoint of an operator, criterion for      VI.9.13—VI.9.14 513
Adjoint of an operator, remarks on      538
Adjoint of an operator, resolvent of      VII.3.7 568
Adjoint of an operator, spectra of      VII.3.7 568 VII.5.9—VII.5.10 VII.5.23
Adjoint of an operator, weakly compact operator      VI.4.7—VI.4.8 484—485
Adjoint space, definition      II.3.7 61
Adjoint space, representation for special spaces      IV.15
Affine mapping, definition      456
Affine mapping, fixed points of      V.10.6 456
Agmon, S.      1161
Agnew, R.P.      87
Ahiezer, N.I.      926 927 929 1269 1270 1272 1273 1274 1276 1588 1589 1590 1592
Ahlfors, L.V.      48
Akilov, G.P.      554
Alaoglu, L.      235 424 462 463 729
Alexandroff theorem on C(S) convergence of bounded additive set functions      IV.9.15 316
Alexandroff theorem on countable additivity of regular set functions on compact spaces      III.5.13 138
Alexandroff, A.D.      138 233 316 380—381 390
Alexandroff, P.      47 467
Alexiewicz, A.      82 83 234 235 392 543
Algebra, algebraic preliminaries      I.10—I.13
Algebra, B*-algebra      IX.3
Algebra, B*-algebra, *-equivalences of B*-algebras      IX.3.4 875
Algebra, B*-algebra, *-homomorphism in      IX.3.4 875
Algebra, B*-algebra, *-isomorphism of      IX.3.4 875
Algebra, B*-algebra, as an algebra of continuous functions      IX.3.7 876
Algebra, B*-algebra, non-commutative      IX.5 884—866
Algebra, B*-algebra, spectrum of      IX.3.4 875
Algebra, B-algebra      Chap. IX
Algebra, B-algebra, as an algebra of continuous functions      IX.2.9 870
Algebra, B-algebra, as an operator algebra      IX.1 860
Algebra, B-algebra, generating set for      IX.2.10 870—871
Algebra, B-algebra, ideal in      IX.1 865—866
Algebra, B-algebra, quotient      IX.1 866
Algebra, B-algebra, radical of      IX.2.5 869
Algebra, B-algebra, semi-simple      IX.2.5 869
Algebra, B-algebra, structure space of      869
Algebra, boolean      see also "Field of sets"
Algebra, Boolean, definition      43
Algebra, Boolean, representation of      44
Algebra, commutative      IX.1.1 860 IX.2
Algebra, definition      40
Algebra, of sets      see "Field of sets"
Algebra, quotient      40
Almost everywhere (or $\mu$ -almost everywhere) definition for additive scalar set functions      III.1.11 100
Almost everywhere (or $\mu$ -almost everywhere) definition for vector-valued set functions      IV.10.6 322
Almost periodic functions, definition      IV.2.25 242
Almost periodic functions, space of, additional properties      IV.15 379
Almost periodic functions, space of, definition      IV.2.25 242
Almost periodic functions, space of, remarks concerning      386—387
Almost periodic functions, space of, study of      IV.7
Almost uniform (or $\mu$ -uniform convergence) definition      III.6.1 145 see
Altman, M.S.      94 609 610
Ambrose, W.      1013 1160 1274
Analytic continuation      230
Analytic function (vector-valued) between complex vector spaces      VI.10.5 522
Analytic function (vector-valued), definition      224
Analytic function (vector-valued), properties      III.14
Analytic function (vector-valued), space of, definition      IV.2.24 242
Analytic function (vector-valued), space of, properties      IV.15
Annihilator of a set      II.4.17 72
Anzai, H.      386
AP      242
Arens' lemma      IX.3.5 875—876
Arens, R.F.      381 382 384 385 396—397 399 466 875 884 886
Arnous, E.      1274
Aronszajn, N.      87 91 234 394 610 928 930 1120
Artemenko, A.      387 392
Arzela theorem on continuity of limit function      IV.6.11 268
Arzela theorem, remarks concerning      383
Arzela, C.      266 268 382 383
Ascoli — Arzela theorem on compactness of continuous functions      IV.6.7 266
Ascoli — Arzela, remarks concerning      382
Ascoli, G.      266 382 460 466
Atkinson, F.V.      610 611 1615
Atom in a measure space      IV.9.6 308
Audin, M.      611
Automorphisms in groups      35
B(s)      240
B*-algebras      IX.3 874—879 see
B-algebra      see "Algebra"
B-space (or Banach space), basic properties of      Chap. II
B-space (or Banach space), definition      II.3.2. 59
B-space (or Banach space), integration      Chap. III
B-space (or Banach space), special B-spaces      Chap. IV
B-space (or Banach space), special B-spaces properties      IV.15
Babenko, K.I.      94 1183
Bade, W.G.      538 612 728 928 1269
Baire category theorem      I.6.9 20
Baire, R.      20
Baker, H.F.      1588
Banach limits, existence and properties      II.4.22—II.4.23 73
Banach theorem on convergence of measurable functions      IV.11.2—IV.11.3 332—334
Banach — Stone theorem on equivalence of C-spaces      V.8.8 442
Banach — Stone, remarks on      396—397 466
Banach, S.      59 62 73 80 81 82—84 85 86 89 91—93 94 234 332 380 385—386 392 442 462—463 465—466 472 538 539 609
Barankin, E.W.      1163
Bari, N.K.      94
Bartle, R.G.      85 92 233 383 386 389 392 539—540 543
Base (or basis)      see also "Hamel base"
Base (or basis) in a B-space, criterion for compactness with      IV.5.5 260
Base (or basis) in a B-space, definition      II.4.7 71
Base (or basis) in a B-space, properties      II.4.8—II.4.12 71
Base (or basis) in a B-space, remarks on      93—94
Base (or basis) in a linear space      see "Hamel base"
Base (or basis), orthogonal and orthonormal bases in Hilbert space, definition      IV.4.11 252
Base (or basis), orthogonal and orthonormal bases in Hilbert space, existence of      IV.4.12 252
Base for a topology, criterion for      I.4.7 11

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