Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T10:59:58.500Z Has data issue: false hasContentIssue false
  • English
  • Français

Deciding eventual positivity of polynomials

Published online by Cambridge University Press:  19 September 2008

David Handelman
David Handelman
Affiliation:
Mathematics Department, University of Ottawa, Ottawa, Ontario K1N 9B4, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let P and f be polynomials in several (real) variables, with P having no negative coefficients. We give necessary and sufficient conditions for there to exist a positive integer n with Pnf having no negative coefficients; roughly speaking, the conditions involve the behaviour of f as a function on the positive orthant, together with its behaviour on a boundary constructed from the supporting monomials of P. This completes a series of results due to Poincaré (1883), Meissner (1911), and Polyà (1927). The former discusses the one variable case, the latter two deal with the situation that the Newton polyhedra of both P and f be, respectively, standard hypercubes, standard simplices.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 57 - 79
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[EHS]Effros, E. G., Handelman, D. E., & Shen, C.-L.. Dimension groups and their affine representations. Amer. J. Math. 102 (1980), 385–407.CrossRefGoogle Scholar
[HI]Handelman, D.. Positive polynomials and product type actions of compact groups.Mem. Amer. Math. Soc. 320 (1985) 79p + xii.Google Scholar
[HR]Handelman, D. & Rossmann, W.. Non-product type actions of compact groups on AF algebras. Illinois J. Math. 29 (1985), 51–95.CrossRefGoogle Scholar