Author | Rickart, Charles E. author |
---|---|
Title | Natural Function Algebras [electronic resource] / by Charles E. Rickart |
Imprint | New York, NY : Springer New York, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8070-2 |
Descript | XIV, 240 p. 1 illus. online resource |
I. The Category of Pairs -- ยง 1. Pairs and systems -- ยง 2. Morphisms and extensions of pairs -- ยง 3. Natural systems -- ยง 4. Products of pairs -- ยง 5. Examples and remarks -- II. Convexity and Naturality -- ยง 6. a-convex hulls. Hull-kernel topology -- ยง 7. a-convexity in a natural pair [?, a] -- ยง 8. Closure operations -- ยง 9. Convexity and extensions -- ยง10. Natural extensions -- ยง11. Examples -- III. The ล ilov Boundary and Local Maximum Principle -- ยง12. Independent points -- ยง13. The ล ilov boundary of a pair -- ยง14. A local maximum principle for natural systems -- ยง15. Applications of the local maximum principle -- IV. Holomorphic Functions -- ยง16. Presheaves of continuous functions -- ยง17. Local extensions, ?-holomo?phic functions -- ยง18. Holomorphic maps -- ยง19. Examples and remarks -- V. Maximum Properties of Holomorphic Functions -- ยง20. A local maximum principle for holomorphic functions -- ยง21. Holomorphic peak sets -- ยง22. a-presheaves -- ยง23. A lemma of Glicksberg -- ยง24. Maximal a-presheaves -- VI. Subharmonic Functions -- ยง25. Plurisubharmonic functions in ?n -- ยง26. Definitions. a-subharmonic functions -- ยง27. Basic properties of a-subharmonic functions -- ยง28. Plurisubharmonicity -- ยง29. Maximum properties -- ยง30. Integral representations -- ยง31. Characterization of a-harmonic functions -- ยง32. Hartogโs functions -- VII. Varieties -- ยง33. Varieties associated with an a-presheaf -- ยง34. Convexity properties -- ยง35. Generalizations of some results of Glicksberg -- ยง36. Continuous families of hypersurfaces -- ยง37. Remarks -- VIII. Holomorphic and Subharmonic Convexity -- ยง38. Convexity with respect to an a-presheaf -- ยง39. Properties of subharmonic convexity -- ยง40. Naturality properties -- ยง41. Holomorphic implied by subharmonic convexity -- ยง42. Local properties -- ยง43. Remarks and an example -- IX. [?, a]-Domains -- ยง44. Definitions -- ยง45. Distance functions -- ยง46. Holomorphic functions -- ยง47. Relative completeness and naturality -- X. Holomorphic Extensions of [?, a]-Domains -- ยง48. Morphisms and extensions. Domains of holomorphy -- ยง49. Existence of maximal extensions -- ยง50. Properties of maximal domains -- ยง51. Remarks -- XI. Holomorphy Theory for Dual Pairs of Vector Spaces -- ยง52. Generalized polynomials and holomorphic functions in a CLTS -- ยง53. Dual pairs ?E, F? -- ยง54. Holomorphic functions in a dual pair -- ยง55. Arens holomorphic functions -- ยง56. Canonical representation of dual pairs -- ยง57. Derivatives -- ยง58. Naturality -- XII. ?E, F? -Domains of Holomorphy -- ยง59. Holomorphic functions in ?E, F?-domains -- ยง60. Subdomains determined by a subspace of F -- ยง61. Envelopes of holomorphy -- ยง62. Series expansions -- ยง63. The finite dimensional component of a domain of holomorphy -- ยง64. The algebra of holomorphic functions -- ยง65. Holomorphic convexity and naturality -- ยง66. A Cartan-Thullen theorem -- XIII. Dual Pair Theory Applied to [?, a]-Domains -- ยง67. The dual pair extension of [?, a]. A-domains -- ยง68. Germ-valued functions -- ยง69. Topologies for [0]? -- ยง70. Naturality of algebras of germ-valued functions -- XIV. Holomorphic Extensions of ?-Domains -- ยง71. Extension relative to germ-valued functions -- ยง72. Uniform families of extensions -- ยง73. Pseudoextensions -- ยง74. Naturality properties -- Index of Symbols -- General Index