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1.

図書

図書
Joseph L. Taylor
出版情報: Providence, R.I. : American Mathematical Society, c2002  xvi, 507 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 46
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Selected problems in one complex variable
Holomorphic functions of several variables
Local rings and varieties
The Nullstellensatz Dimension
Homological algebra Sheaves and sheaf cohomology
Coherent algebraic sheaves
Coherent analytic sheaves Stein spaces
Frechet sheaves-Cartan's theorems
Projective varieties Algebraic vs. analytic-Serre's theorems
Lie groups and their representations
Algebraic groups
The Borel-Weil-Bott theorem
Bibliography
Index
Selected problems in one complex variable
Holomorphic functions of several variables
Local rings and varieties
2.

図書

図書
Toshio Nishino ; translated by Norman Levenberg, Hiroshi Yamaguchi
出版情報: Providence, R.I. : American Mathematical Society, c2001  xiii, 366 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 193
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Fundamental theory: Holomorphic functions and domains of holomorphy
Implicit functions and analytic sets
The Poincare, Cousin, and Runge problems
Pseudoconvex domains and pseudoconcave sets
Holomorphic mappings
Theory of analytic spaces: Ramified domains
Analytic sets and holomorphic functions
Analytic spaces Normal pseudoconvex spaces
Bibliography
Index
Fundamental theory: Holomorphic functions and domains of holomorphy
Implicit functions and analytic sets
The Poincare, Cousin, and Runge problems
3.

図書

図書
M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild
出版情報: Princeton, NJ : Princeton University Press, c1999  xii, 404 p. ; 25 cm
シリーズ名: Princeton mathematical series ; 47
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Preface
Hypersurfaces and Generic Submanifolds in C[superscript N] / Ch. I:
Abstract and Embedded CR Structures / Ch. II:
Vector Fields: Commutators, Orbits, and Homogeneity / Ch. III:
Coordinates for Generic Submanifolds / Ch. IV:
Rings of Power Series and Polynomial Equations / Ch. V:
Geometry of Analytic Discs / Ch. VI:
Boundary Values of Holomorphic Functions in Wedges / Ch. VII:
Holomorphic Extension of CR Functions / Ch. VIII:
Holomorphic Extension of Mappings of Hypersurfaces / Ch. IX:
Segre Sets / Ch. X:
Nondegeneracy Conditions for Manifolds / Ch. XI:
Holomorphic Mappings of Submanifolds / Ch. XII:
Mappings of Real-algebraic Subvarieties / Ch. XIII:
References
Index
Preface
Hypersurfaces and Generic Submanifolds in C[superscript N] / Ch. I:
Abstract and Embedded CR Structures / Ch. II:
4.

図書

図書
Vasiliy Sergeyevich Vladimirov ; with a pref. by N.N. Bogolyubov ; translated by Scripta Technica, Inc. ; edited by Leon Ehrenpreis
出版情報: Mineola : Dover Publications, 2007, c1966  xii, 353 p. ; 22cm
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5.

図書

図書
Steven G. Krantz
出版情報: Providence, RI : American Mathematical Society, 2001, c1992  xvi, 564 p. ; 24 cm
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An introduction to the subject Some integral formulas
Subharmonicity and its applications
Convexity Hormander's solution of the $\bar\partial$ equation
Solution of the Levi problem and other applications of $\bar\partial$ techniques
Cousin problems, cohomology, and sheaves
The zero set of a holomorphic function Some harmonic analysis
Constructive methods Integral formulas for solutions to the $\bar\partial$ problem and norm estimates
Holomorphic mappings and invariant metrics Manifolds
Area measures Exterior algebra Vectors, covectors, and differential forms
List of notation
Bibliography
Index
An introduction to the subject Some integral formulas
Subharmonicity and its applications
Convexity Hormander's solution of the $\bar\partial$ equation
6.

図書

図書
by Pei-Chu Hu and Chung-Chun Yang
出版情報: Dordrecht ; Boston, Mass. : Kluwer Academic, c1999  ix, 338 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 483
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7.

図書

図書
So-Chin Chen, Mei-Chi Shaw
出版情報: Providence, RI : American Mathematical Society, c2001  xii, 380 p. ; 27 cm
シリーズ名: AMS/IP studies in advanced mathematics ; v. 19
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Real and complex manifolds
The Cauchy integral formula and its applications
Holomorphic extension and pseudoconvexity $L^2$ theory for $\overline\partial$ on pseudoconvex domains
The $\overline\partial$-Neumann problem on strongly pseudoconvex manifolds
Boundary regularity for $\overline\partial$ on pseudoconvex domains
Cauchy-Riemann manifolds and the tangential
Cauchy-Riemann complex
Subelliptic estimates for second order differential equations and $\square_b$
The tangential
Cauchy-Riemann complex on pseudoconvex $CR$ manifolds
Fundamental solutions for $\square_b$ on the Heisenberg group
Integral representations for $\overline\partial$ and $\overline\partial_b$
Embeddability of abstract $CR$ structures
Appendix
Bibliography
Table of notation
Index
Real and complex manifolds
The Cauchy integral formula and its applications
Holomorphic extension and pseudoconvexity $L^2$ theory for $\overline\partial$ on pseudoconvex domains
8.

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:
9.

図書

図書
[by] Carl B. Allendoerfer
出版情報: New York : Macmillan, [1974]  xi, 227 p. ; 26 cm
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10.

図書

図書
Heinrich G.W. Begehr and Abduhamid Dzhuraev
出版情報: Harlow : Longman, 1997  454 p. ; 24 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; 88
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