The volume of a region defined by polynomial inequalities
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- by O. S. Rothaus PDF
- Proc. Amer. Math. Soc. 42 (1974), 265-267 Request permission
Abstract:
Let $P(x)$ be a polynomial on ${R^n}$ with nonnegative coefficients. We develop a simple necessary and sufficient condition that the set $S = \{ x \in {R^n}|{x_i} \geqq 0,P(x) \leqq 1\}$ 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.References
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 265-267
- MSC: Primary 52A20
- DOI: https://doi.org/10.1090/S0002-9939-1974-0331219-0
- MathSciNet review: 0331219