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, sλ(x), where λ varies over a fundamental Weyl chamber in R n and x belongs to the positive orthant in R. 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.