Complex analysis in Banach spaces : holomorphic functions and domains of holomorphy in finite and infinite dimensions /

Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of research in infinite dimensional complex analysis. This book presents a uni...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Mujica, Jorge, 1946-
Format: Electronic eBook
Language:Inglés
Published: Amsterdam ; New York : New York, N.Y., U.S.A. : North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1986.
Series:North-Holland mathematics studies ; 120.
Notas de matem�atica (Rio de Janeiro, Brazil) ; no. 107.
Subjects:
Holomorphic functions.
Domains of holomorphy.
Banach spaces.
Fonctions holomorphes.
Domaines d'holomorphie.
Espaces de Banach.
MATHEMATICS > Complex Analysis.
Banach spaces > Holomorphic mappings
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Table of Contents:
  • Front Cover; Complex Analysis in Banach Spaces; Copyright Page; Contents; CHAPTER I. POLYNOMIALS; 1. Multilinear mappings; 2. Polynomials; 3. Polynomials of one variable; 4. Power series; CHAPTER II. HOLOMORPHIC MAPPINGS; 5. Holomorphic mappings; 6. Vector-valued integration; 7. The Cauchy integral formulas; 8. G-holomorphic mappings; 9. The compact-open topology; CHAPTER III. DOMAINS OF HOLOMORPHY; 10. Domains of holomorphy; 11. Holomorphically convex domains; 12. Bounding sets; CHAPTER IV. DIFFERENTIABLE MAPPINGS; 13. Differentiable mappings; 14. Differentiable mappings of higher order
  • 15. Partitions of unity16. Test functions; 17. Distributions; CHAPTER V. DIFFERENTIAL FORMS; 18. Alternating multilinear forms; 19. Differential forms; 20. The Poincars lemma; 21. The? operator; 22. Differential forms with bounded support; 23. The? equation in polydiscs; CHAPTER VI. POLYNOMIALLY CONVEX DOMAINS; 24. Polynomially convex compact sets in Cn; 25. Polynomially convex domains in Cn; 26. Schauder bases; 27. The approximation property; 28. Polynomial approximation in Banach spaces; CHAPTER VII. COMMUTATIVE BANACH ALGEBRAS; 29. Banach algebras; 30. Commutative Banach algebras
  • 31. The joint spectrum32. Projective limits of Banach algebras; 33. The Michael problem; CHAPTER VIII. PLURISUBHARMONIC FUNCTIONS; 34. Plurisubharmonic functions; 35. Regularization of plurisubharmonic functions; 36. Separately holomorphic mappings; 37. Pseudoconvex domains; 38. Plurisubharmonic functions on pseudoconvex domains; CHAPTER IX. THE? EQUATION IN PSEUDOCONVEX DOMAINS; 39. Densely defined operators in Hilbert spaces; 40. The? operator for L 2 differential forms; 41. L2 solutions of the? equation 2; 42. C8 solutions of the? equation; CHAPTER X. THE LEVI PROBLEM
  • 43. The Levi problem in Cn44. Holomorphic approximation in Cn; 45. The Levi problem in Banach spaces; 46. Holomorphic approximation in Banach spaces; CHAPTER XI. RIEMANN DOMAINS; 47. Riemann domains; 48. Distributions on Riemann domains; 49. Pseudoconvex Riemann domains; 50. Plurisubharmonic functions on Riemann domains; 51. The? equation in Riemann domains; CHAPTER XII. THE LEVI PROBLEM IN RIEMANN DOMAINS; 52. The Cartan-Thullen theorem in Riemann domains; 53. The Levi problem in finite dimensional Riemann domains; 54. The Levi problem in infinite dimensional Riemann domains
  • 55. Holomorphic approximation in infinite dimensional Riemann domainsCHAPTER XIII. ENVELOPES OF HOLOMORPHY; 56. Envelopes of holomorphy; 57. The spectrum; 58. Envelopes of holomorphy and the spectrum; BIBLIOGRAPHY; INDEX

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