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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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5.1. 50 5.1. 49 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. 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 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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