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1.

図書
図書
1. Operator analysis : Hilbert space methods in complex analysis (: hardback)
Jim Agler, John Edward McCarthy, Nicholas Young
出版情報: Cambridge : Cambridge University Press, 2020  xv, 375 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 219
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2.

図書
図書
2. Geometric function theory and non-linear analysis
Tadeusz Iwaniec and Gaven Martin
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 2001  xv, 552 p. ; 25 cm
シリーズ名: Oxford mathematical monographs
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3.

図書
図書
3. Linear problems and convexity techniques in geometric function theory
D.J. Hallenbeck and T.H. MacGregor
出版情報: Boston : Pitman, 1984  xvii, 182 p. ; 24 cm
シリーズ名: Monographs and studies in mathematics ; 22
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4.

図書
図書
4. Geometric function theory in several complex variables
Junjiro Noguchi, Takushiro Ochiai ; [translated from the Japanese by Junjiro Noguchi]
出版情報: Providence, R.I. : American Mathematical Society, c1990  xi, 282 p. ; 24 cm
シリーズ名: Translations of mathematical monographs ; v. 80
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Hyperbolic manifolds
Measure hyperbolic manifolds
Positive currents and plurisubharmonic functions
Meromorphic mappings
Nevanlinna theory
Value distribution of holomorphic curves
Hyperbolic manifolds
Measure hyperbolic manifolds
Positive currents and plurisubharmonic functions
5.

図書
図書
5. A history of complex dynamics : from Schröder to Fatou and Julia
Daniel S. Alexander
出版情報: Braunschweig : Vieweg, c1994  vii, 165 p. ; 23 cm
シリーズ名: Aspects of mathematics = Aspekte der Mathematik ; E ; vol. 24
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6.

図書
図書
6. Composition operators and classical function theory (: us : pbk ; : gw : pbk)
Joel H. Shapiro
出版情報: New York ; Berlin : Springer-Verlag, c1993  xvi, 223 p. ; 24 cm
シリーズ名: Universitext ; . Tracts in mathematics
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7.

図書
図書
7. Geometric function theory in one and higher dimensions
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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目次情報: 続きを見る
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：
8.

図書
図書
8. Semigroups in geometrical function theory
by David Shoikhet
出版情報: Dordrecht : Kluwer Academic, c2001  xii, 222 p. ; 25 cm
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目次情報: 続きを見る
Preface
Preliminaries
Notations and notions / 0.1：
Holomorphic functions of a complex variable / 0.2：
Convergence of holomorphic functions / 0.3：
Metric spaces and fixed point principles / 0.4：
The Wolff-Denjoy theory on the unit disk / 1：
Schwarz-Pick Lemma and automorphisms / 1.1：
Boundary behavior of holomorphic self-mappings / 1.2：
Fixed points of holomorphic self-mappings / 1.3：
Fixed point free holomorphic self-mappings of [Delta]. The Denjoy-Wolff Theorem / 1.4：
Commuting family of holomorphic mappings of the unit disk / 1.5：
Hyperbolic geometry on the unit disk and fixed points / 2：
The Poincare metric on [Delta] / 2.1：
Infinitesimal Poincare metric and geodesics / 2.2：
Compatibility of the Poincare metric with convexity / 2.3：
Fixed points of [rho]-nonexpansive mappings on the unit disk / 2.4：
Generation theory on the unit disk / 3：
One-parameter continuous semigroup of holomorphic and [rho]-nonexpansive self-mappings / 3.1：
Infinitesimal generator of a one-parameter continuous semigroup / 3.2：
Nonlinear resolvent and the exponential formula / 3.3：
Monotonicity with respect to the hyperbolic metric / 3.4：
Flow invariance conditions for holomorphic functions / 3.5：
The Berkson-Porta parametric representation of semi-complete vector fields / 3.6：
Asymptotic behavior of continuous flows / 4：
Stationary points of a flow on [Delta] / 4.1：
Null points of complete vector fields / 4.2：
Embedding of discrete time group into a continuous flow / 4.3：
Rates of convergence of a flow with an interior stationary point / 4.4：
A rate of convergence in terms of the Poincare metric / 4.5：
Continuous version of the Julia-Wolff-Caratheodory Theorem / 4.6：
Lower bounds for [rho]-monotone functions / 4.7：
Dynamical approach to starlike and spirallike functions / 5：
Generators on biholomorphically equivalent domains / 5.1：
Starlike and spirallike functions / 5.2：
A generalized Visser-Ostrowski condition and fanlike functions / 5.3：
An invariance property and approximation problems / 5.4：
Hummel's multiplier and parametric representations of starlike functions / 5.5：
A conjecture of Robertson and geometrical characteristics of fanlike functions / 5.6：
Converse theorems on starlike, spirallike and fanlike functions / 5.7：
Growth estimates for spirallike, starlike and fanlike functions / 5.8：
Remarks on Schroeder's equation and the Koenigs embedding property / 5.9：
Bibliography
Author and Subject Index
List of figures
Preface
Preliminaries
Notations and notions / 0.1：
9.

図書
図書
9. Conformal and potential analysis in Hele-Shaw cells
Björn Gustafsson, Alexander Vasilʹev
出版情報: Basel : Birkhäuser Verlag, 2006  x, 231 p. ; 24 cm
シリーズ名: Advances in mathematical fluid mechanics
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10.

図書
図書
10. Schwarz-pick type inequalities (: pbk.)
Farit G. Avkhadiev, Karl-Joachim Wirths
出版情報: Basel : Birkhäuser, c2009  viii, 156 p. ; 24 cm
シリーズ名: Frontiers in mathematics
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目次情報: 続きを見る
Introduction / 1：
Historical remarks / 1.1：
On inequalities for higher derivatives / 1.2：
On methods / 1.3：
Survey of the contents / 1.4：
Basic coefficient inequalities / 2：
Subordinate functions / 2.1：
Bieberbach's conjecture by de Branges / 2.2：
Theorems of Jenkins and Sheil-Small / 2.3：
Inverse coefficients / 2.4：
Domains with bounded boundary rotation / 2.5：
The Poincaré metric / 3：
Background / 3.1：
The Schwarz-Pick inequality / 3.2：
Estimates using the Euclidean distance / 3.3：
An application of Teichmüller's theorem / 3.4：
Domains with uniformly perfect boundary / 3.5：
Derivatives of the conformal radius / 3.6：
Basic Schwarz-Pick type inequalities / 4：
Two classical inequalities / 4.1：
Theorems of Ruscheweyh and Yamashita / 4.2：
Pairs of simply connected domains / 4.3：
Holomorphic mappings into convex domains / 4.4：
Punishing factors for convex pairs / 4.5：
Case n=2 for all domains / 4.6：
Punishing factors for special cases / 5：
Solution of the Chua conjecture / 5.1：
Punishing factors for angles / 5.2：
Sharp lower bounds for punishing factors / 5.3：
Domains in the extended complex plane / 5.4：
Maps from convex into concave domains / 5.5：
Multiply connected domains / 6：
Finitely connected domains / 6.1：
Pairs of arbitrary domains / 6.2：
Some examples / 6.3：
Related results / 7：
Inequalities for schlicht functions / 7.1：
Derivatives of ?-invariant functions / 7.2：
A characterization of convex domains / 7.3：
Some open problems / 8：
The Krzyz conjecture / 8.1：
The angle conjecture / 8.2：
The generalized Goodman conjecture / 8.3：
Bloch and several variable problems / 8.4：
On sums of inverse coefficients / 8.5：
Bibliography
Index
Introduction / 1：
Historical remarks / 1.1：
On inequalities for higher derivatives / 1.2：
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