Let be the real polynomial ring in variables. Pólya’s Theorem says that if a homogeneous polynomial is positive on the standard -simplex , then for sufficiently large all the coefficients of are positive. We give a complete characterization of forms, possibly with zeros on , for which there exists so that all coefficients of have only nonnegative coefficients, along with a bound on the needed.
Journal of Symbolic Computation
Digital Object Identifier (DOI)
Castle, M., Powers, V., & Reznick, B. (2011). Pólya’s Theorem with zeros. Journal of Symbolic Computation, 46(9), 1039-1048. doi:10.1016/j.jsc.2011.05.006