Impossibility of extending Pólya's theorem to "forms" with arbitrary real exponents
Pólya proved that if a form (homogeneous polynomial) with real coefficients is positive on the nonnegative orthant (except at the origin), then it is the quotient of two real forms with no negative coefficients. While Pólya's theorem extends, easily, from ordinary real forms to "generalized" real forms with arbitrary rational exponents, we show that it does not extend to generalized real forms with arbitrary real (possibly irrational) exponents. © 2008 Elsevier B.V. All rights reserved.
Publication Source (Journal or Book title)
Journal of Pure and Applied Algebra
Delzell, C. (2008). Impossibility of extending Pólya's theorem to "forms" with arbitrary real exponents. Journal of Pure and Applied Algebra, 212 (12), 2612-2622. https://doi.org/10.1016/j.jpaa.2008.04.006