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- W2963561573 abstract "Let h:ℝ n →ℝ be a continuous, piecewise-polynomial function. The Pierce-Birkhoff conjecture (1956) is that any such h is representable in the form sup i inf j f ij , for some finite collection of polynomials f ij ∈ℝ[x 1 ,...,x n ]. (A simple example is h(x 1 )=|x 1 |=sup{x 1 ,-x 1 }.) In 1984, L. Mahé and, independently, G. Efroymson, proved this for n≤2; it remains open for n≥3. In this paper we prove an analogous result for “generalized polynomials” (also known as signomials), i.e., where the exponents are allowed to be arbitrary real numbers, and not just natural numbers; in this version, we restrict to the positive orthant, where each x i >0. As before, our methods work only for n≤2." @default.
- W2963561573 created "2019-07-30" @default.
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- W2963561573 date "2010-01-01" @default.
- W2963561573 modified "2023-09-26" @default.
- W2963561573 title "Extension of the Two-Variable Pierce-Birkhoff conjecture to generalized polynomials" @default.
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- W2963561573 doi "https://doi.org/10.5802/afst.1274" @default.
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