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Gelbaum B.R. — Problems in Real and Complex Analysis
Gelbaum B.R. — Problems in Real and Complex Analysis

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Название: Problems in Real and Complex Analysis

Автор: Gelbaum B.R.

Аннотация:

This book builds upon the earlier volume Problems in Analysis, more than doubling it with a new section of problems on complex analysis. The problems on real analysis from the earlier book have all been checked, and stylistic, typographical, and mathematical errors have been corrected. The problems in complex analysis cover most of the principal topics in the theory of functions of a complex variable. The problems in the book cover, in real analysis: set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces; in complex analysis: polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 504

Добавлена в каталог: 14.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\kappa$-ary marker      5.1. 50
$\kappa$-ary representations      5.1. 49
$\kappa$-cylinder      s 6.3. 359
A-measurable      1.2. 9
Abel summation      s 3.1. 217 218 s
Abel, N.H. (lemma)      2.2. 22
Absolutely continuous      3.1. 35 5.1.
Absolutely continuous, (measure)      5.1. 48
Absorbing      6.1. 70
Adhere, adherence, adherent      2.1. 15
Adjoint      6.1. 70 6.2. 6.3.
Alaoglu, L. theorem      s 6.3. 351
Algebra      14.2. 129
Algebra resp. $\sigma$-algebra (of sets)      1.1. 4:
Algebraic number      1.1. 3
Algebraic variety      s 3.3. 207
Analytic (set)      1.2. 7
Analytic continuation      11.1. 115
Anharmonic ratio      7.1. 96
Annulus (A(a, r : R))      9.3. 107
Antipodal      2.3. 25 3.2.
Approximate identity      6.1. 76 s
Area theorem      s 8.1. 386
Arzela, C.-Ascoli, G. theorem      s 2.1. 161
atom      4.1. 40
Auteomorphism      2.1. 19
Autojection      2.2. 22
Automorphism      3.1. 30
Axiom of Choice      s 4.2. 243
Baire, R. category theorem      s 2.2. 169 s
Banach algebra      6.4. 89 s
Banach space      6.3. 84
Banach Steinhaus, H. theorem      s 6.1. 308
Banach, S.      5.1. 59
Base (at a point)      2.1. 13
Base (for a topology)      2.1. 12
Base (for a uniformity)      2.1. 15
Basic neighborhood      2.1. 13 s
Basis      6.1. 71
Bendixson, I.      2.1. 166 2.3.
Bergman, S. kernel function      14.4. 130
Bernstein, S. polynomials      5.1. 258 - 259
Bessel, F. W. inequality      5.1. 251
Biholomorphic bijection      s 13.1. 430
Bijection      5.1. 62
Bijective      2.1. 20
Binary marker      5.1. 50
Biorthogonal      6.3. 86
Birkhoff, G. D. ergodic theorem      5.3. 69 s
Blaschke, W. product      8.2. 105
Bloch, A. theorem      8.2. 129
Block      3.1. 31
Bochner, S. measurable      s 6.3. 358
Borel measure      1.1. 5
Borel set      4.1. 40
Borel, Cantelli, F. P.      5.1. 50
Borel, E.      1.1. 5
Boundary      2.1. 15 9.3.
Bounded      6.1. 70
Bounded, approximate identity      6.3. 90
Bounded, convergence theorem      s 2.3. 183
Branch      11.1. 115
Bridging function      s 6.1. 313
Brouwer, invariance of domain theorem      s 3.3. 216
Brouwer, L. E. J. fixed point theorem      3.3. 39
Cantelli, F. P.      5.1. 50
Cantor (the) function      2.1. 18
Cantor (the) set      2.1. 16
Cantor, G.      2.1. 16
Cantor, like set      2.1. 16
Cantor—Bendixson theorem, cf. BENDIXSON      I.
Cantor—LEBESGUE, H. theorem      5.1. 51
Caratheodory, C. measurable      1.2. 11
Cardinality      1.1. 4
Cartesian product      1.1. 3 2.1.
Category      2.3. 24 29
Cauchy completion      2.1. 16
Cauchy formula      s 7.3. 377
Cauchy net      2.1. 16
Cauchy, A. L. de      2.1. 16
Cauchy, complete      2.2. 16
Central index      10.3. 112
Chain (of indices)      3.1. 31
CHARACTER      6.1. 72
Characteristic function      1.1. 4
Circled      6.1. 70
Closed (with respect to ...)      1.1. 6 2.1.
Closed, ball      2.1. 16
Closed, curve      2.1. 12
Closed, graph theorem      s 6.3. 347
Closed, half-line      s 3.2. 224
Closed, interval      1.1. 3
Closed, set      2.1. 14
Closure      2.1. 12 7.1.
Coarser      2.1. 14
Cofinal      2.1. 14
Compact      1.1. 4
Compact-open      14.2. 127
Complete measure situation      1.2. 11
Complete metric space      2.1. 16 4.1.
Completion (of a $\sigma$-ring)      1.2. 11
Complex measure      1.1. 4
Component      5.1. 60
Concave (function)      4.1. 41
Conditionally convergent      5.1. 50
conformal      10.2. 110
Conjugate bilinear      6.3. 79
Connected      2.1. 14
continuous      2.1. 12
Continuous on the right      15.1. 133
Continuum Hypothesis      s 5.1. 273
Contraction, contractive      2.1. 19
Converge      2.1. 14
Convex function (map)      3.1. 30
Convex function hull      2.3. 25
Convex set      2.3. 25
Convolution      6.1. 72
Coset representative      4.2. 45
Coset space      2.3. 29
Countably additive      1.1.4
Countably determined      2.1. 13
Countably determined, subadditive      4.1. 40
Counting measure      4.1. 40
Cover      2.2. 21
Cover interval      1.1. 3
Cover map      2.1. 12
Cover mapping theorem (for holomorphic functions)      9.3. 109 s s
Cover mapping theorem (for topological vector spaces)      s 6.3. 350 363
Cover set      2.1. 12
Cross ratio      7.1. 96
Curve      2.1. 12
Curve, image      2.1. 12
Cyclic group      s 2.3. 189
Cylinder      2.1. 13
D-separable      5.2. 66
Daniell, measurable      1.2. 8
Daniell, P. J. functional      1.2. 9
Daniell—Stone, M. H. extension      1.2. 7
Degree      2.3. 23
Dense      1.2. 11
Dense in itself      2.1. 14
Derivation      6.4. 90 s
Derivative      3.1. 30
Diagonal sequence      s 2.1. 161 s
Diamond, H.      s 5.1. 289
Differential      3.1. 30 6 84
Dilation      s 7.1. 373
Dini, U. theorem      s 5.1. 265
Direct sum      6.3. 83 6.3. s
Directed downward      4.1. 43
Directed set      2.1. 13
Directed upward      4.1. 44
Dirichlet kernel      5.1. 54
Dirichlet, P G. L. region      s 13.2. 432
Discrete      2.1. 12
Diset      2.1. 13
Distinguished (index)      3.1. 31
Dominated Convergence Theorem      s 1.2. 147
Dual group      6.1. 72
Dual pair      s 6.3 349
Dual space      2.3. 24 6.1.
Dyadic rationed number      s 2.1. 160
Dyadic space      2.1. 18
EGOROV, D. F. theorem      5.1. 53 s
Eigenvalue      6.2. 82
Entire      7.1. 95
Epimorphism      4.2. 46
Equicontinuous      s 3.1. 204
Equidistributed      4.1. 43
Equivalence class      1.1. 4
Equivalence relation      2.1. 14
Equivalent (functions)      6.1. 71
Ergodic theorem (mean)      5.3. 69
Ergodic theorem (pointwise)      5.3. 69 s
Essential supremum      2.3. 24
Essentially bounded      2.3. 24
Essentially equal (nets)      2.1. 14
Euclidean topology      2.1. 20
Euler formula      s 5.1. 261 s
Euler, L. constant      10.3. 114
Even      3.1. 35
Event      5.2. 66
Eventually      2.1. 14
Expansion, expansive      2.1. 19
Expected value      5.2. 66
Exponent divergence      10.3. 112
Exponent of convergence      10.3. 112
Extended complex plane      7.1. 96
Extended real number system      1.2. 7
Extension      6.3. 87
Extreme point      2.3. 25
Fatou, P. lemma      4.1. 41 s s
Fejer theorem      5.1. 267
Fejer, L. kernel      5.1. 54
Fermat, P. de conjecture      s 10.2. 401
Filter      2.1. 14
Filter base      2.1. 14
Filter generated (by)      2.1. 14
Finer (filter)      2.1. 14
Finite Borel partition      s 4.1. 233
Finite cylinder      s 6.3. 359
Finite intersection property      s 2.1. 154 s
Finite rectangle      5.1. 49
Finitely additive      4.1. 42
Finitely determined      2.1. 13
Fixed point      7.1. 98 8
Fourier series      5.1. 54 s
Fourier transform      5.1. 54 6.1. s
Fourier, J. coefficient      5.1. 54
Fourier, Stieltjes, T. J. series      5.1. 55
Fractional part      4.1. 41
Frequently      2.1. 14
Fubini — Tonelli, L. theorem      5.1. 49 s
Fubini, G. theorem      s 3.1. 207
Function lattice      1.2. 7
Function lattice, element      11.1. 115
Fundamental theorem of algebra      s 9.3. 394
Fundamental Theorem of Algebra, Calculus      s 3.1. 203 s s
Gamma function      10.3. 114 11.2.
Gaufiian plane      7.1. 95
Gelfand, I. M.-Fourier, J. transform      6.1. 72
Gelles, G.      s 5.1. 289
Generalized nilpotent      6.4. 90
Generated group      4.2. 46
Gradient      6.2. 79
Gram orthonormalization process      s 3.2. 223 s
Gram, J. P.-Schmidt, E. biorthogonalization process      s 6.3. 348
Graph      2.1. 19 5.1. 6.2.
Greatest integer in      4.1. 41
Green, G. theorem      s 6.2. 332
Gutzmer, A. coefficient estimate      s 7.3. 378 s
Haar, A. measurable, measure, sets      4.2. 44 45
Hadamard three-circles/three-lines theorems      15.2. 132 134
Hadamard, factorization theorem      10.3. 114
Hadamard, gap theorem      11.1. 116
Hadamard, J. determinant estimate      3.2. 39
Hahn open cube, interval      1.1. 3
Hahn space      10.2. III
Hahn — Banach, S. theorem      15.1. 132
Hahn, H. decomposition      s 5.1. 249
Hamel, G. basis      6.3. 84 s
Hardy, G. H. class      14.2. 127
Harmonic conjugate      13.1. 124
Harmonic function      13.1. 124
Harnack theorem      13.2. 126
Harnack, A. inequality      13.2. 125
Hausdorff space resp. topology      2.1. 15 2.2. 21
Hausdorff — Young, G. C. and Young, W. H. theorem      15.2. 135
Hausdorff, F. maximality principle      2.1. 14
Heine, E.-Borel, E. theorem      s 3.1. 194 s
Helly, E. (selection) theorem      s 5.1. 251
hessian      s 3.1. 209
Hilbert, D. space      5.3. 69 6.2.
Hit-index      s 2.1. 157
Holder, O.      15.1. 132
Holomorphic      6.4. 90 7.1.
Homotopic to a constant      7.1. 95
Ideal      2.3. 24 6.4.
Idempotent      6.3. 85
Identity modulo (an ideal)      6.4. 89
Identity theorem (for holomorphic functions)      s 8.1. 382 s s
Immediate analytic continuation      11.1. 115
Improperly Riemann integrable      5.1. 54
Inclusion map      3.2. 38
Independent (events)      5.2. 66
Index (of a curve)      s 9.2. 392
Indivisible      s 1.1. 140
Injective      2.1. 20 8.2.
Inner measure      1.2 146 s
Inner product      6.2. 79
Inner regular      4.1. 40
Integers      1.1. 3
Interior      1.1. 3 2.1.
Intermediate value property      3.1. 31
interval      1.1. 3
Interval function      5.1. 64 s
Inverse function theorem      s 7.3. 377
Involution      6.3. 84—85
Irrational numbers      1.1. 3
Isolated essential singularity      7.3. 99
Isolated point      2.1. 14
Isometric circle      7.1. 98
Isometry      2.1. 19 6.3.
Jacobian      s 6.1. 322 s
Jensen, J. L. W. V. inequality (for convex functions)      4.1. 41
Jensen, J. L. W. V. inequality (for holomorphic functions)      13.2. 125
Kakutani, S.      s 2.3. 191
Kernel      5.1. 54
Kolmogorov, a. N. theorem (for topological vector spaces)      6.4. 89
Krein, M.-Milman, D. theorem      s 6.1. 329
Kronecker lemma      2.3. 24
Kronecker, L. function      s 6.1. 320
Landau, E.      14.3. 129
Laplace, de, P. S. map (Laplacian)      6.2. 79 13.1.
Lattice      1.2. 7
Laurent, P. A. expansion      12.1. 121 s
Lebesgue monotone convergence theorem      s 1.2. 147
Lebesgue set      s 14.2. 438
Lebesgue, H. decomposition      5.1. 48
Left-continuous      2.3. 26
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