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 w eights and coefficients in the exponents, the stability of the weighte d diamond follows from the stability of eight one-parameter families ( edges) of quasi-polynomials. In order to check the diamond for stabili ty, it is sufficient to examine only eight one-parameter families of q uasi-polynomials in contrast to the case of a rectangle of quasi-polyn omials, which requires checking the stability of an exponential number of one-parameter families of quasi-polynomials.