Analyticity in Infinite Dimensional Spaces ( De Gruyter Studies in Mathematics )

Publication series ：De Gruyter Studies in Mathematics

Author： Michel Hervé

Publisher： De Gruyter‎

Publication year： 1989

E-ISBN: 9783110856941

P-ISBN(Paperback): 9783110109955

Subject： O174.3 harmonic functions and potential theory

Language： ENG

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Description

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist.

The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level.

The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.
While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies

Chapter

Chapter 1 Some topological preliminaries

pp.： 1 – 9

Summary

pp.： 9 – 9

1.1 Locally convex spaces

pp.： 9 – 10

1.2 Vector valued infinite sums and integrals

pp.： 10 – 14

1.3 Baire spaces

pp.： 14 – 17

1.4 Barrelled spaces

pp.： 17 – 19

1.5 Inductive limits

pp.： 19 – 21

Chapter 2 Gâteaux-analyticity

pp.： 21 – 27

2.1 Vector valued functions of several complex variables

pp.： 27 – 28

Summary

pp.： 27 – 27

2.2 Polynomials and polynomial maps

pp.： 28 – 36

2.3 Gâteaux-analyticity

pp.： 36 – 43

2.4 Boundedness and continuity of Gâteaux-analytic maps

pp.： 43 – 51

Exercises

pp.： 51 – 58

Chapter 3 Analyticity, or Fréchet-analyticity

pp.： 58 – 59

Summary

pp.： 59 – 59

3.1 Equivalent definitions

pp.： 59 – 60

3.2 Separate analyticity

pp.： 60 – 66

3.3 Entire maps and functions

pp.： 66 – 73

3.4 Bounding sets

pp.： 73 – 81

Exercises

pp.： 81 – 87

Chapter 4 Plurisubharmonic functions

pp.： 87 – 89

4.1 Plurisubharmonic functions on an open set Ω in a I.c. space X

pp.： 89 – 90

Summary

pp.： 89 – 89

4.2 The finite dimensional case

pp.： 90 – 95

4.3 Back to the infinite dimensional case

pp.： 95 – 102

4.4 Analytic maps and pluriharmonic functions

pp.： 102 – 112

4.5 Polar subsets

pp.： 112 – 115

4.6 A fine maximum principle

pp.： 115 – 128

Exercises

pp.： 128 – 135

Chapter 5 Problems involving plurisubharmonic functions

pp.： 135 – 137

Summary

pp.： 137 – 137

5.1 Pseudoconvexity in a I.c. space X

pp.： 137 – 138

5.2 The Levi problem

pp.： 138 – 143

5.3 Boundedness of p.s.h. functions and entire maps

pp.： 143 – 152

5.4 The growth of p.s.h. functions and entire maps

pp.： 152 – 154

5.5 The density number for a p.s.h. function

pp.： 154 – 162

Exercises

pp.： 162 – 170

Chapter 6 Analytic maps from a given domain to another one

pp.： 170 – 171

Summary

pp.： 171 – 171

6.1 A generalization of the Lindelöf principle

pp.： 171 – 172

6.2 Intrinsic pseudodistances

pp.： 172 – 176

6.3 Complex geodesics and complex extremal points

pp.： 176 – 187

6.4 Automorphisms and fixed points

pp.： 187 – 192

Exercises

pp.： 192 – 202

Bibliography

pp.： 202 – 203

Glossary of Notations

pp.： 203 – 209

Subject Index

pp.： 209 – 213

LastPages

pp.： 213 – 217

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