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1.

図書

図書
Ian Graham, Gabriela Kohr
出版情報: New York : Marcel Dekker, c2003  xv, 530 p. ; 24 cm
シリーズ名: Monographs and textbooks in pure and applied mathematics ; 255
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Preface
Introduction
Univalent functions / I:
Elementary properties of univalent functions / 1:
Univalence in the complex plane / 1.1:
Elementary results in the theory of univalent functions. Examples of univalent functions / 1.1.1:
The area theorem / 1.1.2:
Growth, covering and distortion results in the class S / 1.1.3:
The maximum modulus of univalent functions / 1.1.4:
Two-point distortion results for the class S / 1.1.5:
Subclasses of univalent functions in the unit disc / 2:
Functions with positive real part. Subordination and the Herglotz formula / 2.1:
The Caratheodory class. Subordination / 2.1.1:
Applications of the subordination principle / 2.1.2:
Starlike and convex functions / 2.2:
Starlikeness and convexity of order [alpha]. Alpha convexity / 2.3:
Starlikeness and convexity of order [alpha] / 2.3.1:
Alpha convexity / 2.3.2:
Close-to-convexity, spirallikeness and [Phi]-likeness in the unit disc / 2.4:
Close-to-convexity in the unit disc / 2.4.1:
Spirallike functions in the unit disc / 2.4.2:
[Phi]-like functions on the unit disc / 2.4.3:
The Loewner theory / 3:
Loewner chains and the Loewner differential equation / 3.1:
Kernel convergence / 3.1.1:
Subordination chains and kernel convergence / 3.1.2:
Loewner's differential equation / 3.1.3:
Remarks on Bieberbach's conjecture / 3.1.4:
Applications of Loewner's differential equation to the study of univalent functions / 3.2:
The radius of starlikeness for the class S and the rotation theorem / 3.2.1:
Applications of the method of Loewner chains to characterize some subclasses of S / 3.2.2:
Univalence criteria / 3.3:
Becker's univalence criteria / 3.3.1:
Univalence criteria involving the Schwarzian derivative / 3.3.2:
A generalization of Becker's and Nehari's univalence criteria / 3.3.3:
Bloch functions and the Bloch constant / 4:
Preliminaries concerning Bloch functions / 4.1:
The Bloch constant problem and Bonk's distortion theorem / 4.2:
Locally univalent Bloch functions / 4.3:
Distortion results for locally univalent Bloch functions / 4.3.1:
The case of convex functions / 4.3.2:
Linear invariance in the unit disc / 5:
General ideas concerning linear-invariant families / 5.1:
Extremal problems and radius of univalence / 5.2:
Bounds for coefficients of functions in linear-invariant families / 5.2.1:
Radius problems for linear-invariant families / 5.2.2:
Univalent mappings in several complex variables and complex Banach spaces / II:
Univalence in several complex variables / 6:
Preliminaries concerning holomorphic mappings in C[superscript n] and complex Banach spaces / 6.1:
Holomorphic functions in C[superscript n] / 6.1.1:
Classess of domains in C[superscript n]. Pseudoconvexity / 6.1.2:
Holomorphic mappings / 6.1.3:
Automorphisms of the Euclidean unit ball and the unit polydisc / 6.1.4:
Holomorphic mappings in complex Banach spaces / 6.1.5:
Generalizations of functions with positive real part / 6.1.6:
Examples and counterexamples / 6.1.7:
Criteria for starlikeness / 6.2:
Criteria for starlikeness on the unit ball in C[superscript n] or in a complex Banach space / 6.2.1:
Starlikeness criteria on more general domains in C[superscript n] / 6.2.2:
Sufficient conditions for starlikeness for mappings of class C[superscript 1] / 6.2.3:
Starlikeness of order [gamma] in C[superscript n] / 6.2.4:
Criteria for convexity / 6.3:
Criteria for convexity on the unit polydisc and the Euclidean unit ball / 6.3.1:
Necessary and sufficient conditions for convexity in complex Banach spaces / 6.3.2:
Quasi-convex mappings on the unit ball of C[superscript n] / 6.3.3:
Spirallikeness and [Phi]-likeness in several complex variables / 6.4:
Growth, covering and distortion results for starlike and convex mappings in C[superscript n] and complex Banach spaces / 7:
Growth, covering and distortion results for starlike mappings in several complex variables and complex Banach spaces / 7.1:
Growth and covering results for starlike mappings on the unit ball and some pseudoconvex domains in C[superscript n]. Extensions to complex Banach spaces / 7.1.1:
Bounds for coefficients of normalized starlike mappings in C[superscript n] / 7.1.2:
A distortion result for a subclass of starlike mappings in C[superscript n] / 7.1.3:
Growth, covering and distortion results for convex mappings in several complex variables and complex Banach spaces / 7.2:
Growth and covering results for convex mappings / 7.2.1:
Covering theorem and the translation theorem in the case of nonunivalent convex mappings in several complex variables / 7.2.2:
Bounds for coefficients of convex mappings in C[superscript n] and complex Hilbert spaces / 7.2.3:
Distortion results for convex mappings in C[superscript n] and complex Hilbert spaces / 7.2.4:
Loewner chains in several complex variables / 8:
Loewner chains and the Loewner differential equation in several complex variables / 8.1:
The Loewner differential equation in C[superscript n] / 8.1.1:
Transition mappings associated to Loewner chains on the unit ball of C[superscript n] / 8.1.2:
Close-to-starlike and spirallike mappings of type alpha on the unit ball of C[superscript n] / 8.2:
An alternative characterization of spirallikeness of type alpha in terms of Loewner chains / 8.2.1:
Close-to-starlike mappings on the unit ball of C[superscript n] / 8.2.2:
Univalent mappings which admit a parametric representation / 8.3:
Examples of mappings which admit parametric representation on the unit ball of C[superscript n] / 8.3.1:
Growth results and coefficient bounds for mappings in S[superscript 0 subscript g](B) / 8.3.2:
Applications of the method of Loewner chains to univalence criteria on the unit ball of C[superscript n] / 8.4:
Loewner chains and quasiconformal extensions of holomorphic mappings in several complex variables / 8.5:
Construction of quasiconformal extensions by means of Loewner chains / 8.5.1:
Strongly starlike and strongly spirallike mappings of type [alpha] on the unit ball of C[superscript n] / 8.5.2:
Bloch constant problems in several complex variables / 9:
Preliminaries and a generalization of Bonk's distortion theorem / 9.1:
Bloch constants for bounded and quasiregular holomorphic mappings / 9.2:
Bloch constants for starlike and convex mappings in several complex variables / 9.3:
Linear invariance in several complex variables / 10:
Preliminaries concerning the notion of linear invariance in several complex variables / 10.1:
L.I.F.'s and trace order in several complex variables / 10.1.1:
Examples of L.I.F.'s on the Euclidean unit ball of C[superscript n] / 10.1.2:
Distortion results for linear-invariant families in several complex variables / 10.2:
Distortion results for L.I.F.'s on the Euclidean unit ball of C[superscript n] / 10.2.1:
Distortion results for L.I.F.'s on the unit polydisc of C[superscript n] / 10.2.2:
Examples of L.I.F.'s of minimum order on the Euclidean unit ball and the unit polydisc of C[superscript n] / 10.3:
Examples of L.I.F.'s of minimum order on the Euclidean unit ball of C[superscript n] / 10.3.1:
Examples of L.I.F.'s of minimum order on the unit polydisc of C[superscript n] / 10.3.2:
Norm order of linear-invariant families in several complex variables / 10.4:
Norm order and univalence on the Euclidean unit ball of C[superscript n] / 10.5:
Linear-invariant families in complex Hilbert spaces / 10.6:
Univalent mappings and the Roper-Suffridge extension operator / 11:
Convex, starlike and Bloch mappings and the Roper-Suffridge extension operator / 11.1:
Growth and covering theorems associated with the Roper-Suffridge extension operator / 11.2:
Loewner chains and the operator [Phi subscript n, alpha] / 11.3:
Radius problems and the operator [Phi subscript n, alpha] / 11.4:
Linear-invariant families and the operator [Phi subscript n, alpha] / 11.5:
Bibliography
List of Symbols
Index
Preface
Introduction
Univalent functions / I:
2.

図書

図書
Olli Tammi
出版情報: Berlin ; New York : Springer-Verlag, 1978-  v. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 646, 913
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3.

図書

図書
Peter L. Duren
出版情報: New York ; Berlin : Springer-Verlag, c1983  xiv, 382 p. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 259
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4.

図書

図書
by I. M. Milin ; [translated from the Russian by Israel Program for Scientific Translations ; translation edited by P. L. Duren]
出版情報: Providence, R. I. : American Mathematical Society, 1977  iv, 202 p. ; 24 cm
シリーズ名: Translations of mathematical monographs ; v. 49
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5.

図書

図書
Christian Pommerenke, with a chapter on quadratic differentials by Gerd Jensen
出版情報: Göttingen : Vandenhoeck und Ruprecht, 1975  376 p. ; 24 cm
シリーズ名: Studia mathematica/Mathematische Lehrbücher ; Bd. 25
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6.

図書

図書
A.W. Goodman
出版情報: Tampa, FL : Mariner Pub. Co., c1983  2 v. ; 24 cm
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7.

図書

図書
Glenn Schober
出版情報: Berlin ; New York : Springer-Verlag, 1975  iv, 200 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 478
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