Assuming the existence of an analytic interpolant mapping a two-point data from the unit disc $\mathbb{ D}$ to $\widetilde{ \mathbb{ G}}_n$, we describe a class of such interpolating functions where $$\widetilde{ \mathbb{ G}}_n := \{ (y_1,\dots, y_{ n-1}, q)\in \mathbb{ C}^n :\; q \in \mathbb{ D},\; y_{ j} = \beta_{ j} + \bar{ \beta}_{ n-j} q,\; \beta_{ j} \in \mathbb{ C} \; \text{ and } \; |\beta_{ j}|+ |\beta_{ n-j}| < { n \choose j} \; \text{ for } \; j=1,\dots, n-1 \}.$$ We present the connection of $\widetilde{ \mathbb{ G}}_n$ with the $\mu$-synthesis problem.
Categories: math.CV