On stability of a weighted diamond of real quasi-polynomials

This paper deals with the stability problem for a weighted diamond of real quasi-polynomials. We show that under certain conditions on the weights and coefficients in the exponents, the stability of the weighted diamond follows from the stability of eight one-parameter families (edges) of quasi-polynomials. In order to check the diamond for stability, it is sufficient to examine only eight one-parameter families of quasi-polynomials in contrast to the case of a rectangle of quasi-polynomials, which requires checking the stability of an exponential number of one-parameter families of quasi-polynomials.