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On the Gleason problem
Lemmers, F.A.M.O.
Publication date
2002
Link to publication
Citation for published version (APA):
Lemmers, F. A. M. O. (2002). On the Gleason problem.
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Contents s
Prefacee 5
Insteadd of an introduction 9
Chapterr 1. A brief introduction to several complex variables 13
1.1.. Introduction 13 1.2.. On the extension of functions 13
1.3.. Solutions of the <9-problem and their applications 17
Chapterr 2. A survey of the Gleason problem 21 2.1.. Some definitions and examples 21 2.2.. The use of d-techniques 24 2.3.. Counterexamples to the Gleason problem 28
Chapterr 3. Generators and interpolation in algebras of entire functions 31
3.1.. Introduction 31 3.2.. An auxiliary theorem 33
3.3.. The Gleason problem 35 3.4.. Generating the algebra 35 3.5.. An application in interpolation theory 37
Chapterr 4. Solving the Gleason problem on linearly convex domains 39
4.1.. Introduction 39 4.2.. C-convex sets 40 4.3.. Definitions and auxiliary results 40
4.4.. Solving the Gleason problem for if°°(n) 43 4.5.. Extending Ti(f) to the boundary 44
4.6.. Final remarks 46
Chapterr 5. Reinhardt domains and the Gleason problem 47
5.1.. Introduction 47 5.2.. Some definitions, notations and lemmas 47
5.3.. Pseudoconvex Reinhardt domains 50 5.4.. Non-pseudoconvex Reinhardt domains 51
5.5.. An example 55
Chapterr 6. Reinhardt domains with a cusp at the origin 57
6.1.. Introduction 57 6.2.. Definitions 57
88 CONTENTS
6.3.. Solving a Cauchy-Riemann equation 58
6.4.. Auxiliary results 64 6.5.. Dividing ft in two pieces 64
6.6.. Constructing a local solution 65
6.7.. Main result 70 6.8.. The Hartogs triangle and related domains 70
6.9.. If the domain meets one of the coordinate axes 71
6.10.. Final remarks 72 Samenvattingg 73 Importantt notation 77 Indexx 79 Bibliographyy 81 Curriculumm vitae 85 5
