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140122 ||| eng |
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|a 9783034893749
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| 100 |
1 |
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|a Burckel, R.B.
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| 245 |
0 |
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|a An Introduction to Classical Complex Analysis
|h Elektronische Ressource
|b Vol. 1
|c by R.B. Burckel
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| 250 |
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|a 1st ed. 1979
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| 260 |
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|a Basel
|b Birkhäuser
|c 1979, 1979
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| 300 |
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|a 570 p
|b online resource
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| 505 |
0 |
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|a § 3 Applications to Half-planes, Strips and Annuli -- § 4 The Theorem of CarathSodory, Julia, Wolff, et al -- § 5 Subordination -- Notes to Chapter VI -- VII Convergent Sequences of Holomorphic Functions -- § 1 Convergence in H(U) -- § 2 Applications of the Convergence Theorems; Boundedness Criteria -- § 3 Prescribing Zeros -- § 4 Elementary Iteration Theory -- Notes to Chapter VII -- VIII Polynomial and Rational Approximation—Runge Theory -- § 1 The Basic Integral Representation Theorem -- § 2 Applications to Approximation -- § 3 Other Applications of the Integral Representation -- § 4 Some Special Kinds of Approximation -- § 5 Carleman’s Approximation Theorem -- § 6 Harmonic Functions in a Half-plane -- Notes to Chapter VIII -- IX The Riemann Mapping Theorem -- § 1 Introduction -- § 2 The Proof of Caratheodory and Koebe -- § 3 Fejer and Riesz’ Proof -- § 4 Boundary Behavior for Jordan Regions --
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| 505 |
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|a § 5 A Few Applications of the Osgood-Taylor-Caratheodory Theorem -- § 6 More on Jordan Regions and Boundary Behavior -- § 7 Harmonic Functions and the General Dirichlet Problem -- § 8 The Dirichlet Problem and the Riemann Mapping Theorem -- Notes to Chapter IX -- X Simple and Double Connectivity -- § 1 Simple Connectivity -- § 2 Double Connectivity -- Notes to Chapter X -- XI Isolated Singularities -- § 1 Laurent Series and Classification of Singularities -- § 2 Rational Functions -- § 3 Isolated Singularities on the Circle of Convergence -- § 4 The Residue Theorem and Some Applications -- § 5 Specifying Principal Parts—Mittag-Leffler’s Theorem -- § 6 Meromorphic Functions -- § 7 Poisson’s Formula in an Annulus and Isolated Singularities of Harmonic Functions -- Notes toChapter XI -- XII Omitted Values and Normal Families -- § 1 Logarithmic Means and Jensen’s Inequality -- § 2 Miranda’s Theorem -- § 3 Immediate Applications of Miranda --
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| 505 |
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|a § 6 Holomorphic Logarithms Previewed -- Notes to Chapter III -- IV The Index and some Plane Topology -- § 1 Introduction -- § 2 Curves Winding around Points -- § 3 Homotopy and the Index -- § 4 Existence of Continuous Logarithms -- § 5 The Jordan Curve Theorem -- § 6 Applications of the Foregoing Technology -- § 7 Continuous and Holomorphic Logarithms in Open Sets -- § 8 Simple Connectivity for Open Sets -- Notes to Chapter IV -- V Consequences of the Cauchy-Goursat Theorem—Maximum Principles and the Local Theory -- § 1 Goursat’s Lemma and Cauchy’s Theorem for Starlike Regions -- § 2 Maximum Principles -- § 3 The Dirichlet Problem for Disks -- § 4 Existence of Power Series Expansions -- § 5 Harmonic Majorization -- § 6 Uniqueness Theorems -- § 7 Local Theory -- Notes to Chapter V -- VI Schwarz’ Lemma and its Many Applications -- § 1Schwarz’ Lemma and the Conformal Automorphisms of Disks -- § 2 Many-to-one Maps of Disks onto Disks --
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| 505 |
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|a §4 Normal Families and Julia’s Extension of Picard’s Great Theorem -- § 5 Sectorial Limit Theorems -- § 6 Applications to Iteration Theory -- § 7 Ostrowski’s Proof of Schottky’s Theorem -- Notes to Chapter XII -- Name Index -- Symbol Index -- Series Summed -- Integrals Evaluated
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| 505 |
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|a 0 Prerequisites and Preliminaries -- § 1 Set Theory -- § 2 Algebra -- § 3 The Battlefield -- § 4 Metric Spaces -- § 5 Limsup and All That -- § 6 Continuous Functions -- § 7 Calculus -- I Curves, Connectedness and Convexity -- § 1 Elementary Results on Connectedness -- § 2 Connectedness of Intervals, Curves and Convex Sets -- § 3 The Basic Connectedness Lemma -- § 4 Components and Compact Exhaustions -- § 5 Connectivity of a Set -- § 6 Extension Theorems -- Notes to Chapter I -- II (Complex) Derivative and (Curvilinear) Integrals -- § 1 Holomorphic and Harmonic Functions -- § 2 Integrals along Curves -- § 3 Differentiating under the Integral -- § 4 A Useful Sufficient Condition for Differentiability -- Notes to Chapter II -- III Power Series and the Exponential Function -- § 1 Introduction -- § 2 Power Series -- § 3 The Complex Exponential Function -- § 4 Bernoulli Polynomials, Numbers and Functions -- § 5 Cauchy’s Theorem Adumbrated --
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| 653 |
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|a Mathematical analysis
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| 653 |
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|a Analysis
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
0 |
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|a Mathematische Reihe
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| 028 |
5 |
0 |
|a 10.1007/978-3-0348-9374-9
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| 856 |
4 |
0 |
|u https://doi.org/10.1007/978-3-0348-9374-9?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 515
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