UID:
almafu_9958092635402883
Umfang:
1 online resource (321 p.)
ISBN:
1-283-53895-4
,
9786613851406
,
0-08-087217-4
Serie:
North-Holland mathematics studies ; 106
Inhalt:
This book presents a set of basic properties of holomorphic mappings between complex normed spaces and between complex locally convex spaces. These properties have already achieved an almost definitive form and should be known to all those interested in the study of infinite dimensional Holomorphy and its applications.The author also makes ``incursions'' into the study of the topological properties of the spaces of holomorphic mappings between spaces of infinite dimension. An attempt is then made to show some of the several topologies that can naturally be considered in these spaces.〈b
Anmerkung:
Description based upon print version of record.
,
Front Cover; Introduction to Holomorphy; Copyright Page; TABLE OF CONTENTS; FOREWORD; PART I: THE NORMED CASE; CHAPTER 1. NOTATION AND TERMINOLOGY, POLYNOMIALS; CHAPTER 2. POWER SERIES; CHAPTER 3. HOLOMORPHIC MAPPINGS; CHAPTER 4. THE CAUCHY INTEGRAL FORMULAS; CHAPTER 5. CONVERGENCE OF THE TAYLOR SERIES; CHAPTER 6. WEAK HOLOMORPHY; CHAPTER 7. FINITE HOLOMORPHY AND GATEAUX HOLOMORPHY; CHAPTER 8. TOPOLOGIES ON SPACES OF HOLOMORPHIC MAPPINGS; CHAPTER 9. UNIQUENESS OF ANALYTIC CONTINUATION; CHAPTER 10. THE MAXIMUM PRINCIPLE; CHAPTER 11. HOLOMORPHIC MAPPINGS OF BOUNDED TYPE
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CHAPTER 12. DOMAINS OF ab-HOLOMORPHYCHAPTER 13. THE CARTAN-THULLEN THEOREM FOR DOMAINS OF ab-HOLOMORPHY; PART Il: THE LOCALLY CONVEX CASE; CHAPTER 14. NOTATION AND MULTILINEAR MAPPINGS; CHAPTER 15. POLYNOMIALS; CHAPTER 16. TOPOLOGIES ON SPACES OF MULTILINEAR MAPPINGS AND HOMOGENEOUS POLYNOMIALS; CHAPTER 17. FORMAL POWER SERIES; CHAPTER 18. HOLOMORPHIC MAPPINGS; CHAPTER 19. SEPARATION AND PASSAGE TO THE QUOTIENT; CHAPTER 20. B-HOLOMORPHY AND H-HOLOMORPHY; CHAPTER 21. ENTIRE MAPPINGS; CHAPTER 22. SOME ELEMENTARY PROPERTIES OF HOLOMORPHIC MAPPINGS
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CHAPTER 23. HOLOMORPHY, CONTINUITY AND AMPLE BOUNDEDNESSCHAPTER 24. BOUNDING SETS; CHAPTER 25. THE CAUCHY INTEGRAL AND THE CAUCHY INEQUALITIES; CHAPTER 26. THE TAYLOR REMAINDER; CHAPTER 27. COMPACT AND LOCAL CONVERGENCE OF THE TAYLOR SERIES; CHAPTER 28. THE MULTIPLE CAUCHY INTEGRAL AND THE CAUCHY INEQUALITIES; CHAPTER 29. DIFFERENTIALLY STABLE SPACES; CHAPTER 30. LIMITS OF HOLOMORPHIC MAPPINGS; CHAPTER 31. UNIQUENESS OF HOLOMORPHIC CONTINUATION; CHAPTER 32. HOLOMORPHY AND FINITE HOLOMORPHY; CHAPTER 33. THE MAXIMUM SEMINORM THEOREM; CHAPTER 34. PROJECTIVE AND INDUCTIVE LIMITS AND HOLOMORPHY
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CHAPTER 35. TOPOLOGIES ON H(UF); CHAPTER 36. BOUNDED SUBSETS OF SI(U; F); BIBLIOGRAPHY; AN INDEX OF DEFINITIONS; AUTHOR INDEX
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English
Weitere Ausg.:
ISBN 0-444-87666-9
Sprache:
Englisch
Schlagwort(e):
Electronic books
URL:
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