Document Type Master's Dissertation Author De Wet, Pieter Oloff URN etd-07222005-122154 Document Title The division theorem for smooth functions Degree MSc (Mathematics) Department Mathematics and Applied Mathematics Supervisor
Advisor Name Title Prof W L Fouche Committee Chair Keywords
- differential equations partial
- analytic functions
- commutative algebra
- smoothness of functions
Date 2003-04-01 Availability unrestricted AbstractWe discuss Lojasiewicz's beautiful proof of the division theorem for smooth functions. The standard proofs are based on the Weierstrass preparation theorem for analytic functions and use techniques from the theory of partial differential equations. Lojasiewicz's approach is more geometric and syn¬thetic. In the appendices appear new proofs of results which are required for the theorem.
© 2002, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.
Please cite as follows:
De Wet, PO 2002, The division theorem for smooth functions, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-07222005-122154/ >
Filename Size Approximate Download Time (Hours:Minutes:Seconds)
28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access dissertation.pdf 430.90 Kb 00:01:59 00:01:01 00:00:53 00:00:26 00:00:02