UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)
UvA-DARE (Digital Academic Repository)
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.
General rights
It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons).
Disclaimer/Complaints regulations
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.
Preface e
Thiss thesis is the result of four years of research at the department of mathematics att the University of Amsterdam. It started as the logical continuation of the research forr my master thesis. This concerned the question whether a condition on a set off holomorphic functions satisfying certain growth conditions is equivalent to the statementt that the ideal spanned by them is in fact the whole ring of holomorphic functionss satisfying these growth conditions or not. The answer can be found in chapterr 3 : yes, this condition is both necessary and sufficient.
Whilee working on this question, my advisor drew my attention to a problem in the functionn theory of several complex variables, known as the Gleason problem. This alsoo has to do with the structure of ideals in rings of functions. We started to read all thee literature available, made ourselves acquainted with the methods and techniques andd wrote some articles, that are part of this thesis.
Att this place I would like to express my immense gratitude to my advisor, dr. Jan Wiegerinck.. Not only for everything that he learned me, but above all, for his patience andd trust. There were times where he was the only one of us that kept faith, and the timess that he had to listen to (or read something of) a confused mathematician with aa style that is, let's say, not always as clear as it should be, are uncountable.
Thee people in my promotion committee, prof. dr. A. Doelman, dr. A. Fallström, prof.. dr. T.H.K. Koornwinder, prof. dr. J. Korevaar, dr. R.A. Kortram, prof. dr. E.M.. Opdam, dr. P.J.I.M. de Paepe and prof. dr. E.G.F. Thomas surely understand whatt I mean... I thank them, especially Peter de Paepe (who did a very thorough job),, for taking the time to be in this committee, for reading a draft version of this thesiss and for pointing out several mistakes and typos.
Forr helping me out with all my questions, and being a very pleasant roommate for fourr years, I thank Paul Beneker. For playing a part in my life during my PhD years,, sometimes a small one or a short one, but always one that I remember with happinesss and gratitude, I'd like to thank Sharad, Per, Marcel, Guido, Lena, Misja, Natasha,, Erwin, Dirk, Roxana, Ernst, Frank, Bas, Renate, Mariska, Harmen, Anca, Steven,, Nabila, Karel, Annegret, Eelke, Michiel, Andy and Lucas. Those that feel thatt they should be on this list as well I beg for forgiveness; a bad memory and not anyy malicious thoughts caused this unfortunate omission.
Lastt but not least, my beloved family. My parents, brother and sister have always supportedd me, of which I'm very grateful.
Oscarr Lemmers
