Gelbaum B.R. — Problems in Real and Complex Analysis :: Электронная библиотека попечительского совета мехмата МГУ

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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:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1992

Количество страниц: 504

Добавлена в каталог: 14.07.2008

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Предметный указатель

Left-continuous, invariant (Haar) measure      4.2. 44
Leibniz, VON, G. W. rule      s 6.4. 367
Length (Euclidean)      3.1. 30
Length of a curve      3.1. 36 4.1. s
Lexicographic partial order      7.1. 95
Limit point      2.1. 14
Lindelof, E. space      6.2. 345
linear combination      5.3. 67
Linear programming      15.1. 132
Liouville, J. theorem      s 10.1. 398
Lipschitz, R. constant      5.1. 64 s
Locally bounded      6.1. 70
Locally compact      1.1. 4
Locally convex      6.1. 70 s
Locally injective      s 10.2. 402
Log convex      11.2. 119
Lower semicontinuous      2.1. 16
Lower triangular matrix      s 3.2. 223
Maximum Modulus Principle      9.3. 109 s s
Maximum principle (in D relative to B)      15.1. 133
Mean value property      13.1. 124
Mean value theorem      s 2.2. 169
Measurable partition      4.1. 40 6.1. s
Measure isomorphic      5.2. 66
Measure situation      1.1. 4
Meromorphic      11.2. 117 12.1. s
Mesh (of a partition)      s 3.1. 214
Metric density theorem      s 5.1. 266 s
Metrizable      2.1. 19
Metrized      2.1. 19
Middle function      1.2. 7
Middle number      1.2. 7
Midpoint convexity      s 3.1. 199
Minimal base      2.1. 18
Minimal measurable cover      5.1. 52
minimum modulus theorem      s 10.2. 400
Minkowski, H. functional      6.1. 70
Mittag-Leffler, G. theorem      12.3. 123 s s
Mobius, A. F. transformation      7.1. 96
Modular function      4.2. 46
Modular ideal      6.4. 89
Module      6.1. 71
Modulo 1 addition      5.1. 53
Modulo a null set      s 5.1. 252
Modulo column/row operations      s 3.1. 193
Modulus of continuity      3.1. 31
Monodromy theorem      s 10.2. 402
Monotone class      1.1. 4
Monotone class of functions      1.2. 8
Monotone Convergence Theorem      1.2. 10
Monotone space      1.1. 4 2.1.
Monotonely increasing      5.1. 63
Morera, G. theorem      s 11.2. 417 418
Morphism      2.3. 24
Multiplicity      7.3. 99 s s
Mutually singular      5.1. 48
Natural boundary      11.1 116
Natural numbers      1.1. 3
Neighborhood      2.1. 12
Net      2.1. 14
Net—corresponding to a filter      2.1. 15
Neumann, von, J.      5.3. 69 15.1.
Nonatomic      4.1. 40 5.1.
Nonnegative (linear functional)      1.2. 8
Nonoverlapping      s 5.1. 269
Norm      2.3. 24 6.1.
Normal (family of functions)      14.2. 127
Normal (subgroup)      s 2.3. 189
Normal (topology)      s 6.2. 345
Normed vector space      2.3. 24 6.1. 6.2. 6.3.
Nowhere dense      s 2.1. 160 s
Null set      1.2. 11 4.2.
Object      2.3. 29
Odd      2.3. 25 s
Open ball      2.1. 16 3.1. s
Operator norm      2.3. 24 - 25 6.2.
Order (of a group)      s 2.3. 189
Order (of growth)      10.3. 112
Orthogonal projection      6.2. 81 s
Orthonormal      5.1. 51 6.2.
Orthonormal basis      s 5.1. 279
Ostrowski, A. theorem      11.1. 116
Outer measure      1.2. 11 4.1. s
Outer regular (measure)      4.1. 40
P-dimensional Hausdorff measure      4.1. 41
Paracompact      s 6.2. 345
Parseval(-Deschenes), M. A. equation      s 3.2. 222 s6.2.
Partially ordered set      2.1. 13
Partition      3.1. 35
Partition of unity      6.1. 72
Perfect      2.1. 14 20 5.1.
Period      6.3. 85 s
Periodic      s 12.3. 428
Picard, E. (great) theorem      14.3 130 s s
Plancherel, M. theorem      s 5.1. 287 s
Poincare, H. theorem      11.2. 119
Point of condensation      s 9.3. 392
Pointwise ergodic theorem      5.3. 69
POISSON — Jensen, J. L. W. V. formula      13.2. 126
POISSON, S. D. formula      s 13.1. 431 s
Pole      7.3. 99 s
Polynomial      2.3. 26 3.1. 5.1.
POSET      2.1. 13
Positive definite      6.2. 79 s
Positive homogeneous      s 1.2. 149
Positive measure      1.1. 4
Positive part      12.1. 121 s
Principal ideal      2.3. 24 28 14.3.
Principle of the argument      s 9.2. 391
Principles of the maximum and minimum      13.1. 124 - 125
Product measure      5.1. 48
Product topology      2.1. 13 18
Projection (in a Cartesian product)      5.1. 49
Projection (in a Hilbert space)      6.2. 81 s
Quasinorm      6.1. 70
Quaternion      1.1. 3
Quotient group      s 2.3. 189
Quotient norm      6.3. 84
Quotient object      2.3. 29
Quotient space      4.2. 45
Quotient topology      6.3. 83
Rademacher, H. functions      5.3. 68
radiaL      6.1. 70
Radial limit function      8.1. 102
Radical      6.4. 90 s
RADIUS      2.1. 16
Radius of convergence      7.3. 99
Radon, J.-Nikodym, O. derivative      5.1. 48 s
Random variable      5.2. 66
RANGE      2.1. 17
Real algebraic number      1.1. 3
Real irrational number      1.1. 3
Real number      1.1. 3

Real rational number      1.1.3
Rectifiable      2.1. 20
refinement      2.1. 14 21
Refines      2.1. 14
Reflection      7.1. 97
Reflexive Banach space      6.3. 84
Region      6.4. 90 7.1.
Regular function      11.2. 120
Regular ideal      6.4. 89
Regular map      1.1. 6
Regular measure      4.1. 40
Regular point      11.1. 115
Regular space      s 6.2. 345
Relation      2.1. 14
Removable singularity      9.3. 107 12.3 121 122 s
Residue      12.1. 121
Residue theorem      s 11.2. 416
Rouche, E. theorem      s 7.2. 376 s
Row operations      s 3.1. 193
Runge, C. theorem      12.3. 123
Running water lemma      s 3.1. 192
Schauder, J. basis      6.1. 71 6.3.
Schottky, F. theorem      14.4. 130
Schwarz lemma      s 8.1. 382 386 389
Schwarz reflection principle      s 8.1. 382
Schwarz, H. A. formula      13.2. 125
Second category      5.1. 61
Section      5.1. 49 s
Self-dense      2.1. 14
Self-dense kernel      2.1. 14 s
Self-map      s 8.2. 389
Semicontinuous      2.3. 28
Semigroup      4.2. 47
Semigroup with a cancellation law      4.2. 47
Seminorm      6.1. 70
Separable      2.1. 19 20 4.1.
Separable of a topological space, that there is a countable base for its topology, separated      2.1. 14
Separating      2.3. 178
Set function      4.1. 40
Simple arc      s 9.2. 390
Simple closed curve      2.1. 12
Simple function      4.1. 41 s
Simple pole      12.1 121
Simply connected      7.1. 95 9.1. s
Singular part      12.1. 121
Singular point      11.1. 116
Singularity      7.3. 99 12.1.
Span (noun)      5.3. 67
Span (verb)      5.3. 67
Spherically normal      14.4. 127
Step-function      10.3. 113 s
Stereographic projection      7.1. 96
Stieltjes, T. J. measure      s 5.1. 263
Stirling, J. formula      s 10.3. 407
Stone — Weierstrass, K. theorem      2.3. 176
Stone, M. H.      1.2. 7
Stronger, ~est (topology)      2.1. 12
Subadditive      1.2. 10 s
Subcover      2.2. 21
Subharmonic      15.1. 133
Subordinate      6.1. 72
subspace      5.3. 67
Subsum      2.2. 22
Superadditive      s 4.1. 225
Support (of a function)      1.1. 4
Support (of a measure)      5.1. 48
Supporting line      3.1. 30 s
Surjection      2.1. 18 s
Surjective      6.2. 82 s 156
Suslin, M. [Souslin, M.]      1.2. 7
Symmetric difference      5.1. 48
Szpilrajn, E.      s 1.2. 146
ternary      5.1. 50
The $\sigma$ -ary representation      5.1. 50
The Cantor function      2.1. 18
The Cantor set Co      2.1. 16
The Cantor-like set Ca      2.1. 16
Theory of games      15.1. 132
Thick      s 4.4. 243
Thorin, G. O. theorem      15.1. 132 s
Tietze, H. extension theorem      s 3.1. 214
Toeputz, O. matrix      2.2. 23
Topological field      2.3. 24 3.1. 6.1.
Topological group      2.1. 15 2.3.
Topological semigroup      4.2. 47
Topological vector space      3.1. 30 6.1.
Totally bounded      s 6.3. 353
Totally disconnected      3.1. 36
Totally finite      1.1. 5
Transcendental      10.2. 110
Transfinite induction (principle)      s 1.1. 140—141
Transitive      2.1. 13
translate      2.3. 26
Translation-invariant      2.3. 27 6.2. s s
Triangle inequality      s 3.2. 223
Trivial topology      2.1. 12
Type (of its order)      10.3. 112
Ultrafilter      2.1. 14
Uniform boundedness principle      s 2.3. 187 s s
Uniformity situation      2.1. 15
Uniformly continuous      2.2. 21
Uniformly convex      6.1. 71
Uniformly integrable      5.1. 49
Unimodular      4.2. 46
Unit ball      6.1. 77
Unit sphere      3.1. 35
Unitary      5.3. 69 6.2.
Univalent      s 10.2. 400
Upper semicontinuous      2.1. 16 2.3.
Urysohn, P. lemma      4.1. 43 s
Vandermonde, A. T.      s 2.2. 172
Vanishing at infinity      1.1. 4
Variance      5.2. 66
Variation      3.1. 35
Vitali, G. theorem      s 9.3. 392 396 s
Walsh, J. L. functions      5.3. 68
Weak basis      6.1. 71
Weierstrass factorization (product) theorem      10.3. 112 s
Weierstrass — CASORATI, F. theorem      s 10.2. 399
Weierstrass, K. approximation theorem      s 2.2. 172 s 5.1.
Weight      2.1. 18
Weil, A., topology      s 4.2. 247
Well-ordered      1.1. 4
Well-ordering Axiom      2.1. 14
Weyl, H. equidistribution theorem      4.1. 43
Wiener, N.-Tauber, A. theorem      s 6.2. 346
Winding number      s 9.2. 391
WlRTlNGER, W. inequality      3.2. 38
Young, G. C.-Young, W. H. theorem      15.2 135
ZERMELO, E.-Fraenkel, A. A. axiom system for set theory      4.2. 243
Zero object      2.3. 29
Zero-one law      5.3. 67
Zeta function      11.2. 118
ZORN, M. lemma      2.1. 14

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