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Gelbaum B.R. — Problems in Real and Complex Analysis
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Название: Problems in Real and Complex AnalysisАвтор: 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 ed2k: ed2k stats Год издания: 1992Количество страниц: 504Добавлена в каталог: 14.07.2008Операции: Положить на полку |
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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 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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