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1.

図書

図書
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
出版情報: Berlin : Springer, c2001  x, 259 p. ; 24 cm
シリーズ名: Grundlehren text editions / editors, A. Chenciner ... [et al.] ; managing editors, M. Berger, J. Coates, S.R.S. Varadhan
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目次情報: 続きを見る
Preface
Introduction: Notation, Elementary Results / 0:
Some Facts About Lower and Upper Bounds / 1:
The Set of ExtendedReal Numbers / 2:
Linear and Bilinear Algebra / 3:
Differentiationin a Euclidean Space / 4:
Set-Valued Analysis / 5:
Recalls on Convex Functions of the Real Variable / 6:
Exercises
Convex Sets / A:
Generalities
Definition and First Examples / 1.1:
Convexity-PreservingOperationsonSets / 1.2:
ConvexCombinationsandConvexHulls / 1.3:
ClosedConvexSetsandHulls / 1.4:
ConvexSetsAttachedtoaConvexSet
TheRelativeInterior / 2.1:
TheAsymptoticCone / 2.2:
ExtremePoints / 2.3:
Exposed Faces / 2.4:
ProjectionontoClosedConvexSets
TheProjectionOperator / 3.1:
ProjectionontoaClosedConvexCone / 3.2:
Separation and Applications
SeparationBetweenConvexSets / 4.1:
First Consequences of the Separation Properties / 4.2:
Existence of Supporting Hyperplanes
Outer Description of Closed ConvexSets
Proof of Minkowski's Theorem
Bipolar of a ConvexCone
The Lemma of Minkowski-Farkas / 4.3:
ConicalApproximationsofConvexSets
ConvenientDefinitions of Tangent Cones / 5.1:
TheTangentandNormalConestoaConvexSet / 5.2:
SomePropertiesofTangentandNormalCones / 5.3:
Convex Functions / B:
Basic Definitions and Examples
The Definitions of a ConvexFunction
Special Convex Functions: Affinity and Closedness
Linear and Affine Functions
ClosedConvexFunctions
OuterConstructionofClosedConvexFunctions
FirstExamples
FunctionalOperationsPreservingConvexity
OperationsPreservingClosedness
Dilations and Perspectives of a Function
Infimal Convolution
Image of a Function Under a Linear Mapping
Convex Hull and Closed Convex Hull of a Function / 2.5:
Local and Global Behaviour of a Convex Function
Continuity Properties
Behaviour at Infinity
First- and Second-Order Differentiation
Differentiable ConvexFunctions
Nondifferentiable Convex Functions
Second-Order Differentiation
Sublinearity and Support Functions / C:
SublinearFunctions
Definitions and First Propertie
SomeExamples
TheConvexConeofAllClosedSublinearFunctions
The Support Function of a Nonempty Set
Definitions, Interpretations
BasicProperties
Examples
Correspondence Between Convex Sets and Sublinear Functions
The Fundamental Correspondence
Example: Norms and Their Duals, Polarity
Calculus with Support Functions / 3.3:
Example: Support Functions of Closed Convex Polyhedra / 3.4:
Subdifferentials of Finite Convex Functions / D:
The Subdifferential: Definitions and Interpretations
First Definition: Directional Derivatives
Second Definition: Minorizationby Affine Functions
GeometricConstructionsandInterpretations
Local Properties of the Subdifferential
First-OrderDevelopments
Minimality Conditions
Mean-ValueTheorems
Calculus Rules with Subdifferentials
Positive Combinations of Functions
Pre-Composition with an Affine Mapping
Post-Composition with an Increasing Convex Function of Several Variables
Supremum of Convex Functions / 4.4:
FurtherExamples / 4.5:
Largest Eigenvalue of a Symmetric Matrix
NestedOptimization
Best Approximation of a Continuous Function on a Compact Interval
The Subdifferential as a Multifunction
Monotonicity Properties of the Subdifferential / 6.1:
Continuity Properties of the Subdifferential / 6.2:
Subdifferentials and Limits of Subgradients / 6.3:
Conjugacy in Convex Analysis / E:
The Convex Conjugate of a Function
Interpretations
FirstProperties
-Elementary Calculus Rules
-The Biconjugate of a Function
-ConjugacyandCoercivity
Subdifferentials of Extended-Valued Functions
Calculus Rules on the Conjugacy Operation
Sum of Two Functions
Infima and Suprema
Post-Composition with an Increasing Convex Function
Various Examples
The Cramer Transformation
The Conjugate of Convex Partially Quadratic Functions
PolyhedralFunctions
Differentiability of a Conjugate Function
First-Order Differentiability
Lipschitz Continuity of the Gradient Mapping
Bibliographical Comments
The Founding Fathers of the Discipline
References
Index
Preface
Introduction: Notation, Elementary Results / 0:
Some Facts About Lower and Upper Bounds / 1:
2.

図書

図書
by A.G. Kusraev, S.S. Kutateladze
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1995  ix, 398 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 323
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3.

図書

図書
Ilya J. Bakelman
出版情報: Berlin ; New York : Springer-Verlag, c1994  xxi, 510 p. ; 25 cm
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4.

図書

図書
Roger Webster
出版情報: Oxford ; Tokyo : Oxford University Press, 1994  xvii, 444 p. ; 24 cm
シリーズ名: Oxford science publications
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5.

図書

図書
by Constantin Udrişte
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1994  xv, 348 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 297
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6.

図書

図書
by Karl-Hermann Neeb
出版情報: Berlin : Walter de Gruyter, 2000, c1999  xxi, 778 p. ; 25 cm
シリーズ名: De Gruyter expositions in mathematics ; v. 28
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Preface
Introduction
Abstract Representation Theory / A.:
Reproducing Kernel Spaces / Chapter I.:
Operator-Valued Positive Definite Kernels / I.1.:
The Cone of Positive Definite Kernels / I.2.:
Representations of Involutive Semigroups / Chapter II.:
Involutive Semigroups / II.1.:
Bounded Representations / II.2.:
Hermitian Representations / II.3.:
Representations on Reproducing Kernel Spaces / II.4.:
Positive Definite Functions on Involutive Semigroups / Chapter III.:
Positive Definite Functions--the Discrete Case / III.1.:
Enveloping C*-algebras / III.2.:
Multiplicity Free Representations / III.3.:
Continuous and Holomorphic Representations / Chapter IV.:
Continuous Representations and Positive Definite Functions / IV.1.:
Holomorphic Representations of Involutive Semigroups / IV.2.:
Convex Geometry and Representations of Vector Spaces / B.:
Convex Sets and Convex Functions / Chapter V.:
Convex Sets and Cones / V.1.:
Finite Reflection Groups and Convex Sets / V.2.:
Convex Functions and Fenchel Duality / V.3.:
Laplace Transforms / V.4.:
The Characteristic Function of a Convex Set / V.5.:
Representations of Cones and Tubes / Chapter VI.:
Commutative Representation Theory / VI.1.:
Representations of Cones / VI.2.:
Holomorphic Representations of Tubes / VI.3.:
Realization of Cyclic Representations by Holomorphic Functions / VI.4.:
Holomorphic Extensions of Unitary Representations / VI.5.:
Convex Geometry of Lie Algebras / C.:
Convexity in Lie Algebras / Chapter VII.:
Compactly Embedded Cartan Subalgebras / VII.1.:
Root Decompositions / VII.2.:
Lie Algebras With Many Invariant Convex Sets / VII.3.:
Convexity Theorems and Their Applications / Chapter VIII.:
Admissible Coadjoint Orbits and Convexity Theorems / VIII.1.:
The Structure of Admissible Lie Algebras / VIII.2.:
Invariant Elliptic Cones in Lie Algebras / VIII.3.:
Highest Weight Representations of Lie Algebras, Lie Groups, and Semigroups / D.:
Unitary Highest Weight Representations: Algebraic Theory / Chapter IX.:
Generalized Highest Weight Representations / IX.1.:
Positive Complex Polarizations / IX.2.:
Highest Weight Modules of Finite-Dimensional Lie Algebras / IX.3.:
The Metaplectic Factorization / IX.4.:
Unitary Highest Weight Representations of Hermitian Lie Algebras / IX.5.:
Unitary Highest Weight Representations: Analytic Theory / Chapter X.:
The Convex Moment Set of a Unitary Representation / X.1.:
Irreducible Unitary Representations / X.2.:
The Metaplectic Representation and Its Applications / X.3.:
Special Properties of Unitary Highest Weight Representations / X.4.:
Moment Sets for C*-algebras / X.5.:
Moment Sets for Group Representations / X.6.:
Complex Ol'shanskii Semigroups and Their Representations / Chapter XI.:
Lawson's Theorem on Ol'shanskii Semigroups / XI.1.:
Holomorphic Extension of Unitary Representations / XI.2.:
Holomorphic Representations of Ol'shanskii Semigroups / XI.3.:
Irreducible Holomorphic Representations / XI.4.:
Gelfand-Raikov Theorems for Ol'shanskii Semigroups / XI.5.:
Decomposition and Characters of Holomorphic Representations / XI.6.:
Realization of Highest Weight Representations on Complex Domains / Chapter XII.:
The Structure of Groups of Harish-Chandra Type / XII.1.:
Representations of Groups of Harish-Chandra Type / XII.2.:
The Compression Semigroup and Its Representations / XII.3.:
Examples / XII.4.:
Hilbert Spaces of Square Integrable Holomorphic Functions / XII.5.:
Complex Geometry and Representation Theory / E.:
Complex and Convex Geometry of Complex Semigroups / Chapter XIII.:
Locally Convex Functions and Local Recession Cones / XIII.1.:
Invariant Convex Sets and Functions in Lie Algebras / XIII.2.:
Calculations in Low-Dimensional Cases / XIII.3.:
Biinvariant Plurisubharmonic Functions / XIII.4.:
Complex Semigroups and Stein Manifolds / XIII.5.:
Biinvariant Domains of Holomorphy / XIII.6.:
Biinvariant Hilbert Spaces and Hardy Spaces on Complex Semigroups / Chapter XIV.:
Biinvariant Hilbert Spaces / XIV.1.:
Hardy Spaces Defined by Sup-Norms / XIV.2.:
Hardy Spaces Defined by Square Integrability / XIV.3.:
The Fine Structure of Hardy Spaces / XIV.4.:
Coherent State Representations / Chapter XV.:
Complex Structures on Homogeneous Spaces / XV.1.:
Heisenberg's Uncertainty Principle and Coherent States / XV.2.:
Appendices
Bounded Operators on Hilbert Spaces / Appendix I.:
Spectral Measures and Unbounded Operators / Appendix II.:
Holomorphic Functions on Infinite-Dimensional Spaces / Appendix III.:
Symplectic Geometry / Appendix IV.:
Simple Modules of p-Length 2 / Appendix V.:
Symplectic Modules of Convex Type / Appendix VI.:
Square Integrable Representations of Locally Compact Groups / Appendix VII.:
The Stone-von Neumann-Mackey Theorem / Appendix VIII.:
Bibliography
List of Symbols
Index
Preface
Introduction
Abstract Representation Theory / A.:
7.

図書

図書
Marián J. Fabian
出版情報: New York : Wiley, c1997  xi, 180 p. ; 25 cm
シリーズ名: Canadian Mathematical Society series of monographs and advanced texts
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Canonical Examples of Weak Asplund Spaces
Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces
Stegall's Classes
Two More Concrete Classes of Banach Spaces that Lie in S
Fragmentability
"Long Sequences" of Linear Projections
Vasak Spaces and Gul'ko Compacta
A Characterization of WCG Spaces and of Eberlein Compacta
Main Open Questions and Problems
References
Index
Canonical Examples of Weak Asplund Spaces
Properties of Gateaux Differentiability Spaces and Weak Asplund Spaces
Stegall's Classes
8.

図書

図書
Ivan Singer
出版情報: New York : John Wiley & Sons, c1997  xix, 491 p. ; 25 cm
シリーズ名: Canadian Mathematical Society series of monographs and advanced texts
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Abstract Convexity of Elements of a Complete Lattice
Abstract Convexity of Subsets of a Set
Abstract Convexity of Functions on a Set
Abstract Quasi-Convexity of Functions on a Set
Dualities Between Complete Lattices
Dualities Between Families of Subsets
Dualities Between Sets of Functions
Conjugations. (-Dualities and <$$$>-Dualities
Abstract Subdifferentials
Notes and Remarks
References
Indexes
Abstract Convexity of Elements of a Complete Lattice
Abstract Convexity of Subsets of a Set
Abstract Convexity of Functions on a Set
9.

図書

図書
Jean-Baptiste Hiriart-Urruty, Claude Lemaréchal
出版情報: Berlin ; New York ; Tokyo : Springer-Verlag, c1993  2 v. ; 25 cm
シリーズ名: Die Grundlehren der mathematischen Wissenschaften ; 305, 306
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10.

図書

図書
by Michael J. Panik
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1993  xxii, 294 p. ; 25 cm
シリーズ名: Theory and decision library ; series B . Mathematical and statistical methods ; v. 24
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