Functions of one complex variable II / John B. Conway.
Series Graduate texts in mathematics ; 159Editor: New York : Springer-Verlag, c1995Descripción: xvi, 394 p. ; 24 cmISBN: 0387944605Otro título: Functions of one complex variable 2 | Functions of one complex variable twoOtra clasificación: 30-01 (31A05 31A15)13 Return to Basics [1] 1 Regions and Curves [1] 2 Derivatives and Other Recollections [6] 3 Harmonic Conjugates and Primitives [14] 4 Analytic Arcs and the Reflection Principle [16] 5 Boundary Values for Bounded Analytic Functions [21] 14 Conformal Equivalence for Simply Connected Regions [29] 1 Elementary Properties and Examples [29] 2 Crosscuts [33] 3 Prime Ends [40] 4 Impressions of a Prime End [45] 5 Boundary Values of Riemann Maps [48] 6 The Area Theorem [56] 7 Disk Mappings: The Class S [61] 15 Conformal Equivalence for Finitely Connected Regions [71] 1 Analysis on a Finitely Connected Region [71] 2 Conformal Equivalence with an Analytic Jordan Region [76] 3 Boundary Values for a Conformal Equivalence Between Finitely Connected Jordan Regions [81] 4 Convergence of Univalent Functions [85] 5 Conformal Equivalence with a Circularly Slit Annulus [90] 6 Conformal Equivalence with a Circularly Slit Disk [97] 7 Conformal Equivalence with a Circular Region [100] 16 Analytic Covering Maps [109] 1 Results for Abstract Covering Spaces [109] 2 Analytic Covering Spaces [113] 3 The Modular Function [116] 4 Applications of the Modular Function [123] 5 The Existence of the Universal Analytic Covering Map [125] 17 De Branges’s Proof of the Bieberbach Conjecture [133] 1 Subordination [133] 2 Loewner Chains [136] 3 Loewner’s Differential Equation [142] 4 The Milin Conjecture [148] 5 Some Special Functions [156] 6 The Proof of de Branges’s Theorem [160] 18 Some Fundamental Concepts from Analysis [169] 1 Bergman Spaces of Analytic and Harmonic Functions [169] 2 Partitions of Unity [174] 3 Convolution in Euclidean Space [177] 4 Distributions [185] 5 The Cauchy Transform [192] 6 An Application: Rational Approximation [196] 7 Fourier Series and Cesàro Sums [198] 19 Harmonic Functions Redux [205] 1 Harmonic Functions on the Disk [205] 2 Fatou’s Theorem [210] 3 Semicontinuous Functions [217] 4 Subharmonic Functions [220] 5 The Logarithmic Potential [229] 6 An Application: Approximation by Harmonic Functions [235] 7 The Dirichlet Problem [237] 8 Harmonic Majorants [245] 9 The Green Function [246] 10 Regular Points for the Dirichlet Problem [253] 11 The Dirichlet Principle and Sobolev Spaces [259] 20 Hardy Spaces on the Disk [269] 1 Definitions and Elementary Properties [269] 2 The Nevanlinna Class [272] 3 Factorization of Functions in the Nevanlinna Class [278] 4 The Disk Algebra [286] 5 The Invariant Subspaces of Hp [290] 6 Szegö’s Theorem [295] 21 Potential Theory in the Plane [301] 1 Harmonic Measure [301] 2 The Sweep of a Measure [311] 3 The Robin Constant [313] 4 The Green Potential [315] 5 Polar Sets [320] 6 More on Regular Points [328] 7 Logarithmic Capacity: Part 1 [331] 8 Some Applications and Examples of Logarithmic Capacity [339] 9 Removable Singularities for Functions in the Bergman Space [344] 10 Logarithmic Capacity: Part 2 [352] 11 The Transfinite Diameter and Logarithmic Capacity [355] 12 The Refinement of a Subharmonic Function [360] 13 The Fine Topology [367] 14 Wiener’s criterion for Regular Points [376]
| Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 30 C767-2 (Browse shelf) | Available | A-7487 | ||||
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 30 C767-2 (Browse shelf) | Ej. 2 | Available | A-8111 |
Continuación de: Functions of one complex variable, part I. 2nd. ed. Springer, 1978.
Bibliografía: p. [384]-388.
13 Return to Basics [1] --
1 Regions and Curves [1] --
2 Derivatives and Other Recollections [6] --
3 Harmonic Conjugates and Primitives [14] --
4 Analytic Arcs and the Reflection Principle [16] --
5 Boundary Values for Bounded Analytic Functions [21] --
14 Conformal Equivalence for Simply Connected Regions [29] --
1 Elementary Properties and Examples [29] --
2 Crosscuts [33] --
3 Prime Ends [40] --
4 Impressions of a Prime End [45] --
5 Boundary Values of Riemann Maps [48] --
6 The Area Theorem [56] --
7 Disk Mappings: The Class S [61] --
15 Conformal Equivalence for Finitely Connected Regions [71] --
1 Analysis on a Finitely Connected Region [71] --
2 Conformal Equivalence with an Analytic Jordan Region [76] --
3 Boundary Values for a Conformal Equivalence Between Finitely --
Connected Jordan Regions [81] --
4 Convergence of Univalent Functions [85] --
5 Conformal Equivalence with a Circularly Slit Annulus [90] --
6 Conformal Equivalence with a Circularly Slit Disk [97] --
7 Conformal Equivalence with a Circular Region [100] --
16 Analytic Covering Maps [109] --
1 Results for Abstract Covering Spaces [109] --
2 Analytic Covering Spaces [113] --
3 The Modular Function [116] --
4 Applications of the Modular Function [123] --
5 The Existence of the Universal Analytic Covering Map [125] --
17 De Branges’s Proof of the Bieberbach Conjecture [133] --
1 Subordination [133] --
2 Loewner Chains [136] --
3 Loewner’s Differential Equation [142] --
4 The Milin Conjecture [148] --
5 Some Special Functions [156] --
6 The Proof of de Branges’s Theorem [160] --
18 Some Fundamental Concepts from Analysis [169] --
1 Bergman Spaces of Analytic and Harmonic Functions [169] --
2 Partitions of Unity [174] --
3 Convolution in Euclidean Space [177] --
4 Distributions [185] --
5 The Cauchy Transform [192] --
6 An Application: Rational Approximation [196] --
7 Fourier Series and Cesàro Sums [198] --
19 Harmonic Functions Redux [205] --
1 Harmonic Functions on the Disk [205] --
2 Fatou’s Theorem [210] --
3 Semicontinuous Functions [217] --
4 Subharmonic Functions [220] --
5 The Logarithmic Potential [229] --
6 An Application: Approximation by Harmonic Functions [235] --
7 The Dirichlet Problem [237] --
8 Harmonic Majorants [245] --
9 The Green Function [246] --
10 Regular Points for the Dirichlet Problem [253] --
11 The Dirichlet Principle and Sobolev Spaces [259] --
20 Hardy Spaces on the Disk [269] --
1 Definitions and Elementary Properties [269] --
2 The Nevanlinna Class [272] --
3 Factorization of Functions in the Nevanlinna Class [278] --
4 The Disk Algebra [286] --
5 The Invariant Subspaces of Hp [290] --
6 Szegö’s Theorem [295] --
21 Potential Theory in the Plane [301] --
1 Harmonic Measure [301] --
2 The Sweep of a Measure [311] --
3 The Robin Constant [313] --
4 The Green Potential [315] --
5 Polar Sets [320] --
6 More on Regular Points [328] --
7 Logarithmic Capacity: Part 1 [331] --
8 Some Applications and Examples of Logarithmic Capacity [339] --
9 Removable Singularities for Functions in the Bergman Space [344] --
10 Logarithmic Capacity: Part 2 [352] --
11 The Transfinite Diameter and Logarithmic Capacity [355] --
12 The Refinement of a Subharmonic Function [360] --
13 The Fine Topology [367] --
14 Wiener’s criterion for Regular Points [376] --
MR, 96i:30001
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