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Zygmund A. — Trigonometric Series. Volume 2

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Название: Trigonometric Series. Volume 2

Автор: Zygmund A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1959

Количество страниц: 358

Добавлена в каталог: 12.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$D_{n}$ , $\tilde{D}_{n}$       49
$D_{n}^{*}$ , $\tilde{D}_{n}^{*}$       50
$I_{n}(x, f)$       4
$K_{n}$       83
,       14
      96
      96
$S_{n}(x; f)$ , $S_{n}(x; f)$       49
$S_{n}^{*}(x; f)$ , $S_{n}^{*}(x; f)$       50
$\Delta(r, t)$       96
$\mathfrak_{V}^{*}$       123
$\mathfrak{A} [f; a, b]$       16
$\mathfrak{M}[f;a, b]$       16
$\mathfrak{S}_{r}$       16
$\mathfrak{U}$ , $\mathfrak{U}_{r}^{*}$       124
$\mathfrak{V}$       120
$\sigma_{n}(x; f)$       89
$\textsf{S}[f]$ , $\tilde{\textsf{S}}[f]$       7
$\textsf{S}^{(k)}[f]$       40
$\textsf{S}_{n}[f]$ , $\tilde{\textsf{S}}_{n}[f]$       49
$\tilde{K}_{n}$       91
Approximation, best      115
Arc associated      202 320
Arc opposite      99
Area (of an image)      290
Basis      234
Bound, essential (upper, lower)      18 94
Boundary, extremal (distinguished      315
Boundedness (C, $\alpha$ )      76
Capacity, $\alpha$       195
Capacity, $\lambda$       194
Capacity, logaritlimic      155
Capacity, outer $\alpha$       195
Coefficients of a trigonometric series      1
Coefficients, Fourier (sine, cosine, complex)      5 11 300
Coefficients, Fourier — Lagrange      6
Coefficients, Fourier — Stieiltjes      11
Coefficients, lacunary      181
Condition of regularity (i), (ii), (iii)      74
Condition, A, B, B ${}^{\prime}$ , C (for kernels)      75 76
Condition, B      199
Condition, Dini      171
Condition, E      98
Condition, Lipschitz      42
Convergence in $L^{r}$       20
Convergence, almost      184
Convergence, factors      93
Convergence, of order Convergence,       373
Convergence, restricted      309
Convergence, stable      216
Convergence, uniform at a point      58
Convergence, uniform semi      174
Convolution (composition)      36 38
Cylinder, unit -      315
Derivative, approximate, symmetric approximate      324
Derivative, fractional      134
Derivative, generalized -th (symmetric, de la Vail $\acute{e}$ e — Poussin)      59
Derivative, generalized -th (unsymmetric, Peano)      59
Derivative, Schwarz (Riemann)      23
Derivative, strong      305
Derivative, symmetric (first and second)      22
Derivative, upper and lower      23
Dirichlet problem      97
EDGE      315
Equiconvergence      53
Equiconvergence, in the wider sense      53
Euler’s constant      15
Extension, parabolic (of functions)      73
Factors of type (P; Q)      176
Formula, Fourier’s inversion      247
Formula, Green’s      260
Formula, Jensen’s      272
Formula, Mellin’s inversion      254
Formula, Parseval — Placherel’s      248
Formula, Parseval’s      13 37 157
Formula, Poisson’s summation      68
Functional      164
Functions (classes of), $B^{(k)}$ , $C^{(k)}$       73
Functions (classes of), $E^{\sigma}$       272
Functions (classes of), $H^{p}$       271
Functions (classes of), $L^{r}$ , $L_{\phi}$ , $\phi(L)$ , $L^{\alpha}$ $(log+L)^{\beta}$       16
Functions (classes of), $L_{\Phi}^{*}$       170
Functions (classes of), $N_{\alpha}$       316
Functions (classes of), $\Lambda_{\alpha}$ , $\lambda_{\alpha}$ , $\Lambda_{*}$ , $\lambda_{*}$       42 43
Functions (classes of), $\Lambda_{\alpha}^{\nu}$ , $\lambda_{\alpha}^{\nu}$ , $\Lambda_{*}^{\nu}$ , $\lambda_{*}^{\nu}$       45
Functions (classes of), $\mathfrak{H}^{r}$       29
Functions (classes of), A, B, C      136
Functions (classes of), complementary      157
Functions (classes of), N      71 316
Functions (classes of), N ${}^{\prime}$       282
Functions (classes of), R      142
Functions (classes of), V      136
Functions,       210
Functions, $\gamma$ , $\gamma_{1}$ , $\gamma_{3}$       222 223
Functions, $\mu$       219
Functions, associated (with a point, set)      4
Functions, asymptotically equal      14
Functions, asymptotically Gauss distributed      264
Functions, characteristic of a transformation      168
Functions, complementary in the sense of Young      16
Functions, Conjugate      51 243
Functions, conjugate of order       63
Functions, convex (concave)      51
Functions, distribution      29 262
Functions, equidistributed      29
Functions, Gauss distributed      264
Functions, Lebesgue      195
Functions, logarithmically convex      25
Functions, major, minor      327
Functions, of a distribution function      262
Functions, of bounded deviation      229
Functions, of jumps      259
Functions, of monotonic type      64
Functions, of order 1 and 2      87
Functions, of the same order      14
Functions, periodic      8 301
Functions, s      207
Functions, simple      94
Functions, slowly varying      186
Functions, smooth      13
Functions, smooth of order       63
Functions, trapezoidal      10
Functions, triangular (roof)      10
Functions, uniformly absolutely continuous      144
Functions, uniformly integrable R      15
Functions, Weierstrass      47
Gauss distribution      264
Gibbs’s phenomenon      61 110
Inequality, Bessel’s      13
Inequality, H $\ddot{o}$ lder’s      17 175
Inequality, Jensen’s      21 94
Inequality, Minkowski’s      18
Inequality, triangle      162
Inequality, Young’s      17
integral      8 232
Integral, $M^{2}$       86
Integral, conjugate      282
Integral, Denjoy’s Integral, special (Perron’s)      84
Integral, Fourier’s single      242
Integral, fractional (Riemann — Liouville, Weyl)      133 139
Integral, Laplace      244
Integral, M      84
Integral, normalized second indefinite      87
Integral, Poisson’s      83 303
Integral, repeated      214
Integral, trigonometric      244
Interpolation, abscissa, oxdinate of      2
Interpolation, Hermite      23
Interpolation, Lagrange      23
Kernel, conjugate      49

Kernel, Dirichlet      49
Kernel, Dirichlet modified      50
Kernel, Fej $\acute{e}$ r      88
Kernel, Fej $\acute{e}$ r, conjugate      93
Kernel, mortified conjugate      50
kernel, Poisson      96
Kernel, Poisson, conjugate      96
Kernel, positive      86
Kernel, quasi-positive      86
Lebesgue constants      67
Lemmas, Fatou’s      26
Lemmas, Rajchman’s      353
Lemmas, van der Corput’s      197
Limit, approximate      323
localization      52
Localization, for cross-neighbourhoods      305
Localization, for interpolation      17
Localization, Riemann principle of      330 367
Localization, Riemann — Lebesgue principle of      53
Mass distribution      11
Matrix, positive      75
Matrix, regular, triangular      74
Maximum (minimum) of a function at a point      88
Means, arithmetic (C, $\alpha$ )      76
Means, delayed (C, 1)      80
Means, integral arithmetic      83 69
Means, linear      74
Modulus of continuity      42
Modulus of continuity, integral      46
Neighbourhoods, cross      306
Neighbourhoods, symmetric      199
Neighbourhoods, symmetric and similar      318
Neighbourhoods, triangular      199 318
Non-tangential paths      81
Norm      163
Norm, weak, strong      111
Normal system      6
Number of roots of a polynomial      2
Numbers, Ces $\grave{a}$ ro ( $A^{\alpha}_{n}$ )      76
Numbers, S      148
Operation (Transformation), linear, continuous, bounded      164
Operation (Transformation), multilinear      106
Operation (Transformation), of strong, weak type (, )      111
Order of a polynomial      1
Partial sums, modified      60
Partial sums, rectangular, spherical      302
Partial sums, symmetric      2
Points, fundamental (nodal)      1
Points, of strong density      307
Points, opposite      99
Polynomials, adjusted      26
Polynomials, Bernoulli’s      42
Polynomials, fundamental      1
Polynomials, interpolating      1
Polynomials, interpolating of the second kind      23
Polynomials, Jackson’s      22
Polynomials, power      1
Polynomials, trigonometric      1
Portion      28
Principal value      61
Products, formal, Blaschke      274
Products, formal, of integrals      282
Products, formal, of series      330
Products, formal, Riesz      208
Property $\beta_{k}$       73
Property $\beta_{k}$ , D      44
Restricted behaviour of a function      321
Restricted convergence, summability      309
Riemann theory of trigonometric series      316
Sequence, convex      93
Sequence, of bounded variation      4
Series, conjugate      1
Series, Fourier      6 300
Series, Fourier trigonometric (sine, cosine, complex)      7
Series, Fourier — Stieltjes      11
Series, generalized Fourier sine series      48
Series, lacunary      202
Series, of class S; trigonometric      1
Series, of Hardy and Littlewood      197
Series, of power series type      3
Series, of Salem      225
Series, orthogonal      6
Series, power series of bounded variation      286
Series, Rademacher      212
Series, randomly continuous      219
Series, with ‘small’ gape      222
Sets, Cantor      196
Sets, classes of, $H^{(m)}$       346
Sets, classes of, $H^{(m)}_{*}$       152
Sets, classes of, $H_{\sigma}$       318
Sets, classes of, $M_{s}$       348
Sets, classes of, $M_{s}$ , $M_{i}$ , $M_{i^{\prime}}$       295
Sets, classes of, $U^{*}$       360
Sets, classes of, $U_{s}$ , $U_{i}$ , $U_{i^{\prime}}$       295
Sets, classes of, $U_{s}^{*}$ , $U_{i}^{*}$       296
Sets, classes of, H      317
Sets, classes of, M      344
Sets, classes of, N, $N_{s}$       236
Sets, classes of, U      344
Sets, classes of, U( $\epsilon$ )      351
Sets, dense, non-dense, everywhere dense      28 162
Sets, denumerable      9
Sets, in the restricted sense      348
Sets, in the wide sense      160
Sets, Lebesgue (for functions)      66
Sets, of circular structure      178
Sets, of constant ratio of dissection      196
Sets, of first and second categories      28 162
Sets, of multiplicity      344
Sets, of type N, $N_{s}$       236
Sets, of uniqueness      344
Sets, simply connected      290
Spaces, $l^{p}$ , $L^{p}$       163
Spaces, Banach      163
Spaces, complete      162
Spaces, linear      162
Spaces, measure      94
Spaces, metric      162
Spaces, normed      163
Spaces, Orlicz      170
Spaces, separable      162
Sum, Ces $\grave{a}$ ro      76
Summability, $A^{*}$       303
Summability, $H_{e}$       181
Summability, $L_{n}$       321
Summability, $R_{r}$       69
Summability, (C, $\alpha$ )      76
Summability, (C, 1)      302
Summability, A (Abel or Poisson)      80 302
Summability, absolute      83
Summability, by the logarithmic mean      106
Summability, C      66
Summability, of type U      333
Summability, R      319
Summability, restricted      309
Summability, strong (C, 1)      181
Summation by parts      3
Systems, closed      127
Systems, closed, complete      5
Systems, closed, orthogonal, Systems, closed, orthonormal      6
Systems, closed, trigonometric (complex)      7
Systems, closed, with respect to      6
Test, Dini      62
Test, Dini — Lipechitz      63
Test, Dirichlet — Jordan      67
Test, Lebesgue      66
Theorems, Banach — Steinhaus      166
Theorems, Bary      349
Theorems, Bernstein      240 11 276
Theorems, Cantor — Lebesgue      316

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