Complex Analysis in Locally Convex Spaces

Name: Complex Analysis in Locally Convex Spaces
Brand: Elsevier
Price: 175.0 EUR
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S. Dineen(Autor*in)

Elsevier (Verlag)

Erschienen am 18. August 2011

491 Seiten

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978-0-08-087168-4 (ISBN)

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Front Cover
Complex Analysis in Locally Convex Spaces
Copyright Page
CONTENTS
FOREWORD
CHAPTER 1. POLYNOMIALS ON LOCALLY CONVEX TOPOLOGICAL VECTOR SPACES
1.1 Algebraic properties of polynomials
1.2 Continuous polynomials
1.3 Topologies on spaces of polynomials
1.4 Duality theory for spaces of polynomials
1.5 Exercises
1.6 Notes and Remarks
CHAPTER 2. HOLOMORPHIC MAPPINGS BETWEEN LOCALLY CONVEX SPACES
2.1 Gâteaux holomorphic mappings
2.2 Holomorphic mappings between locally convex spaces
2.3 Locally convex topologies on spaces of holomorphic Function mapping
2.4 Germs of holomorphic functions
2.5 Exercises
2.6 Notes and Remarks
CHAPTER 3. HOLOMORPHIC FUNCTIONS ON BALANCED SETS
3.1 Associated topologies and generalized decompositions in locally convex spaces
3.2 Equi-Schauder decompositions of (H(U
F),)
3.2 Equi-Schauder decompositions of (H(U
F) , ? )
3.3 Application of generalised decompositions to the study of holomorphic functions on balanced open sets
3.4 Semi-reflexivity and nuclearity for spaces of holomorphic functions
3.5 Exercises
3.6 Notes and Remarks
CHAPTER 4. HOLOMORPHIC FUNCTIONS ON BANACH SPACES
4.1 Analytic equalities and inequalities
4.2 Bounding subsets of a Banach space
4.3 Holomorphic functions on Banach spaces with an unconditional basis
4.4 Further results and examples concerning holomorphic functions on Banach spaces
4.5 Exercises
4.6 Notes and Remarks
CHAPTER 5. HOLOMORPHIC FUNCTIONS ON NUCLEAR SPACES WITH A BASIS
5.1 Nuclear spaces with a basis
5.2 Holomorphic functions on fully nuclear spaces with a basis
5.3 Holomorphic functions on DN spaces with a basis
5.4 Topological properties inherited by strict inductive limits and subspaces
5.5 Exercises
5.6 Notes and Remarks
CHAPTER 6. GERMS, SURJECTIVE LIMITS, ? -PRODUCTS AND POWER SERIES SPACES
6.1 Holomorphic germs on compact sets
6.2 Surjective limits of locally convex spaces
6.3 ?-Products
6.4 Power series spaces of infinite type
6.5 Exercises
6.6 Notes and Remarks
APPENDIX I: FURTHER DEVELOPMENTS IN INFINITE DIMENSIONAL HOLOMORPHY
APPENDIX II: DEFINITIONS AND RESULTS FROM FUNCTIONAL ANALYSIS, SEVERAL COMPLEX VARIABLES AND TOPOLOGY
APPENDIX III: NOTES ON SOME EXERCISES
Bibliography
Index

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