Analyticity in infinite dimensional spaces
Michel Hervé.
Bok Engelsk 1989 · Electronic books.
| Utgitt | Berlin ; New York : : W. de Gruyter, , 1989.
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| Omfang | 1 online resource (216 p.)
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| Opplysninger | Description based upon print version of record.. - Chapter 1 Some topological preliminaries; Summary; 1.1 Locally convex spaces; 1.2 Vector valued infinite sums and integrals; 1.3 Baire spaces; 1.4 Barrelled spaces; 1.5 Inductive limits; Chapter 2 Gâteaux-analyticity; Summary; 2.1 Vector valued functions of several complex variables; 2.2 Polynomials and polynomial maps; 2.3 Gâteaux-analyticity; 2.4 Boundedness and continuity of Gâteaux-analytic maps; Exercises; Chapter 3 Analyticity, or Fréchet-analyticity; Summary; 3.1 Equivalent definitions; 3.2 Separate analyticity; 3.3 Entire maps and functions; 3.4 Bounding sets; Exercises. - Chapter 4 Plurisubharmonic functionsSummary; 4.1 Plurisubharmonic functions on an open set Ω in a I.c. space X; 4.2 The finite dimensional case; 4.3 Back to the infinite dimensional case; 4.4 Analytic maps and pluriharmonic functions; 4.5 Polar subsets; 4.6 A fine maximum principle; Exercises; Chapter 5 Problems involving plurisubharmonic functions; Summary; 5.1 Pseudoconvexity in a I.c. space X; 5.2 The Levi problem; 5.3 Boundedness of p.s.h. functions and entire maps; 5.4 The growth of p.s.h. functions and entire maps; 5.5 The density number for a p.s.h. function; Exercises. - Chapter 6 Analytic maps from a given domain to another oneSummary; 6.1 A generalization of the Lindelöf principle; 6.2 Intrinsic pseudodistances; 6.3 Complex geodesics and complex extremal points; 6.4 Automorphisms and fixed points; Exercises; Bibliography; Glossary of Notations; Subject Index
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| Emner | |
| Sjanger | |
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| ISBN | 0899252052. - 3110109956
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