Positivity of multivariate complex interval rational functions

摘要

The robustness of multivariate complex interval positive rational functions is studied. One of the main points made by S. Basu (1990) is on the robustness of the positive complex (PC) property for an n-variate complex interval rational function. Basu concluded that the PC property of the specific 16(2/sup n/)/sup 2/ extreme members of the set can imply the PC property of the set. In this work, it is proved that the PC property of an interval set of n-variate complex rational functions can be assured by the PC property of its certain 16(2/sup n/) extreme members which are a subset of those 16(2/sup n/)/sup 2/ extreme members defined by Basu.