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New Zealand Mathematics Colloquium 1999
July 6-9, 1999
Department of Mathematics and Statistics, University of Canterbury
Christchurch, New Zealand

Organizers
Doris Barnard, Therese Boustead, Chris Price, Bruce Robson, Gunter Steinke, Graeme Wake, Allan Willms

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A Calculus Problem from Ring Theory
by
R. Raphael
Concordia University, Montreal
Coauthors: P. Olver (University of Minesota)

The following notion arose in studying rings of quotients of rings of continuous functions. A real-valued function f defined on a topological space is called absolutely polynomial if its absolute value can be written as a polynomial in f with continuous coefficients. While many real functions are absolutely polynomial, we provide a number of interesting explicit examples which are not. The notion turns out to be quite delicate, admitting a general theory.

The (not so trivial) starting point was a question one could ask of a first year calculus class.

Date received: May 31, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacc-28.