Open Access
1999/2000 The Absolute Value of Functions
Peter J. Olver, Robert Raphael
Real Anal. Exchange 25(1): 257-290 (1999/2000).


A real-valued function $f$ defined on a topological space is called {\is absolutely polynomial} if its absolute value can be written as a polynomial in $f$ with continuous coefficients. One motivation for studying such functions comes from the theory of rings of continuous functions. While many real functions are absolutely polynomial, we provide a number of interesting explicit examples which are not. The absolutely polynomial criterion turns out to be quite delicate, and we develop the theory in some detail. Our study of absolutely polynomial functions is then widened to more general topological spaces. Our results provide pertinent counterexamples in the theory of rings of quotients of $\Phi$--algebras.


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Peter J. Olver. Robert Raphael. "The Absolute Value of Functions." Real Anal. Exchange 25 (1) 257 - 290, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.26004
MathSciNet: MR1758006

Primary: 26A06 , 26A15 , 26A45 , ‎54C30 , 54H10

Keywords: absolutely polynomial , Bounded variation , continuity , phi-algebra , real-valued function , ring of quotients

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
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