Spectral density functions of bivariable stable polynomials

Abstract

The relationship between a stable multivariable polynomial $p(z)$ and the Fourier coefficients of its spectral density function $1/|p(z)|^2$, is further investigated. In this paper we focus on the radial asymptotics of the Fourier coefficients for a specific choice of a two variable polynomial. Hypergeometric functions appear in the analysis, and new results are derived for these as well.