Author(s): Jorge Alberto Barroso
Series: North-Holland Mathematics Studies 106
Publisher: Elsevier Science Ltd
Year: 1985
Language: English
Pages: 320
Introduction to Holomorphy......Page 4
Copyright Page......Page 5
TABLE OF CONTENTS......Page 14
FOREWORD......Page 8
PART I: THE NORMED CASE......Page 16
CHAPTER 1. NOTATION AND TERMINOLOGY, POLYNOMIALS......Page 18
CHAPTER 2. POWER SERIES......Page 34
CHAPTER 3. HOLOMORPHIC MAPPINGS......Page 42
CHAPTER 4. THE CAUCHY INTEGRAL FORMULAS......Page 48
CHAPTER 5. CONVERGENCE OF THE TAYLOR SERIES......Page 62
CHAPTER 6. WEAK HOLOMORPHY......Page 74
CHAPTER 7. FINITE HOLOMORPHY AND GATEAUX HOLOMORPHY......Page 86
CHAPTER 8. TOPOLOGIES ON SPACES OF HOLOMORPHIC MAPPINGS......Page 98
CHAPTER 9. UNIQUENESS OF ANALYTIC CONTINUATION......Page 128
CHAPTER 10. THE MAXIMUM PRINCIPLE......Page 132
CHAPTER 11. HOLOMORPHIC MAPPINGS OF BOUNDED TYPE......Page 136
CHAPTER 12. DOMAINS OF ab-HOLOMORPHY......Page 144
CHAPTER 13. THE CARTAN-THULLEN THEOREM FOR DOMAINS OF ab-HOLOMORPHY......Page 156
CHAPTER 14. NOTATION AND MULTILINEAR MAPPINGS......Page 174
CHAPTER 15. POLYNOMIALS......Page 178
CHAPTER 16. TOPOLOGIES ON SPACES OF MULTILINEAR MAPPINGS AND HOMOGENEOUS POLYNOMIALS......Page 186
CHAPTER 17. FORMAL POWER SERIES......Page 192
CHAPTER 18. HOLOMORPHIC MAPPINGS......Page 196
CHAPTER 19. SEPARATION AND PASSAGE TO THE QUOTIENT......Page 202
CHAPTER 20. B-HOLOMORPHY AND H-HOLOMORPHY......Page 204
CHAPTER 21. ENTIRE MAPPINGS......Page 206
CHAPTER 22. SOME ELEMENTARY PROPERTIES OF HOLOMORPHIC MAPPINGS......Page 210
CHAPTER 23. HOLOMORPHY, CONTINUITY AND AMPLE BOUNDEDNESS......Page 214
CHAPTER 24. BOUNDING SETS......Page 216
CHAPTER 25. THE CAUCHY INTEGRAL AND THE CAUCHY INEQUALITIES......Page 228
CHAPTER 26. THE TAYLOR REMAINDER......Page 234
CHAPTER 27. COMPACT AND LOCAL CONVERGENCE OF THE TAYLOR SERIES......Page 240
CHAPTER 28. THE MULTIPLE CAUCHY INTEGRAL AND THE CAUCHY INEQUALITIES......Page 248
CHAPTER 29. DIFFERENTIALLY STABLE SPACES......Page 252
CHAPTER 30. LIMITS OF HOLOMORPHIC MAPPINGS......Page 256
CHAPTER 31. UNIQUENESS OF HOLOMORPHIC CONTINUATION......Page 260
CHAPTER 32. HOLOMORPHY AND FINITE HOLOMORPHY......Page 264
CHAPTER 33. THE MAXIMUM SEMINORM THEOREM......Page 268
CHAPTER 34. PROJECTIVE AND INDUCTIVE LIMITS AND HOLOMORPHY......Page 272
CHAPTER 35. TOPOLOGIES ON H(U;F)......Page 282
CHAPTER 36. BOUNDED SUBSETS OF SI(U;F)......Page 292
BIBLIOGRAPHY......Page 298
AN INDEX OF DEFINITIONS......Page 316
AUTHOR INDEX......Page 320
