Log-convexity properties of Schur functions and generalized hypergeometric functions of matrix argument

We establish a positivity property for the difference of products of certain Schur functions, s_λ(x), where λ varies over a fundamental Weyl chamber in ℝⁿ and x belongs to the positive orthant in ℝⁿ. Further, we generalize that result to the difference of certain products of arbitrary numbers of Schur functions. We also derive a log-convexity property of the generalized hypergeometric functions of two Hermitian matrix arguments, and we show how that result may be extended to derive higher-order log-convexity properties.