A Calculus Problem from Ring Theory
by
Robert Raphael
Concordia University
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: December 14, 1998