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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The volume of a region defined by polynomial inequalities

Author: O. S. Rothaus
Journal: Proc. Amer. Math. Soc. 42 (1974), 265-267
MSC: Primary 52A20
MathSciNet review: 0331219
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Abstract: Let $ P(x)$ be a polynomial on $ {R^n}$ with nonnegative coefficients. We develop a simple necessary and sufficient condition that the set $ S = \{ x \in {R^n}\vert{x_i} \geqq 0,P(x) \leqq 1\} $ shall have finite volume. A corresponding result where $ P(x)$ is replaced by a collection of polynomials is an easy corollary. Finally, the necessary and sufficient conditions for the special case that P is a product of linear forms is also given.

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PII: S 0002-9939(1974)0331219-0
Article copyright: © Copyright 1974 American Mathematical Society

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