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1.

図書
図書
1. Convex analysis : an introductory text (pbk.)
Jan van Tiel
出版情報: Chichester [West Sussex] ; New York : Wiley, c1984  viii, 125 p. ; 24 cm
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2.

図書
図書
2. Convex analysis and variational problems (: us ; : ne)
Ivar Ekeland, Roger Temam
出版情報: Amsterdam : North-Holland Pub. Co. , New York : distributors for the U.S.A., American Elsevier Pub. Co., 1976  ix, 402 p. ; 23 cm
シリーズ名: Studies in mathematics and its applications ; v. 1
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3.

図書
図書
3. Convex analysis and optimization
ed. by J.P. Aubin & R.B. Vinter
出版情報: Boston : Pitman Advanced Pub. Program, c1982  210 p. ; 25 cm
シリーズ名: Research notes in mathematics ; 57
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目次情報: 続きを見る
Ioffe's fans and generalized derivatives of vector-valued maps / J.-P. Aubin
A review of continuity and differentiability properties of quasiconvex functions on (Rn) / J.-P. Crouzeix
Ioffe's mean value theorem / I. Ekeland
(E-) subdifferential calculus / J.-B. Hiriart-Urruty
Non-smooth analysis and the theory of fans / A.D. Ioffe
The invariance of the absolute Borel classes / J.E. Jayne and C.A. Rogers
Convex functions arising in optimal control, and Ioffe's global optimally conditions / R.B. Vinter
New applications of generalized curves, particularly in physics/ L.C. Young
Ioffe's fans and generalized derivatives of vector-valued maps / J.-P. Aubin
A review of continuity and differentiability properties of quasiconvex functions on (Rn) / J.-P. Crouzeix
Ioffe's mean value theorem / I. Ekeland
4.

図書
図書
4. Holomorphy and convexity in Lie theory
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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目次情報: 続きを見る
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.：
5.

図書
図書
5. Convex analysis and global optimization
by Hoang Tuy
出版情報: Dordrecht : Kluwer Academic Publishers, c1998  xi, 339 p. ; 25 cm
シリーズ名: Nonconvex optimization and its applications ; v. 22
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6.

図書
図書
6. Abstract convex analysis
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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目次情報: 続きを見る
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
7.

図書
図書
7. Convex functions
A. Wayne Roberts, Dale E. Varberg
出版情報: New York : Academic Press, 1973  xx, 300 p. ; 23 cm
シリーズ名: Pure and applied mathematics ; 57
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8.

図書
図書
8. Gâteaux differentiability of convex functions and topology : weak asplund spaces
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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目次情報: 続きを見る
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
9.

図書
図書
9. Foundations of mathematical optimization : convex analysis without linearity
by Diethard Pallaschke and Stefan Rolewicz
出版情報: Dordrecht ; Boston : Kluwer Academic, c1997  xii, 582 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 388
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10.

図書
図書
10. Subdifferentials : theory and applications
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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