Interpolating functions for a family of domains related to $\mu$-synthesis

Abstract

Assuming the existence of an analytic interpolant mapping a two-point data from the unit disc $\mathbb{D}$ to ${\tilde{\mathbb{G}}}_n$, we describe a class of such interpolating functions where $${\tilde{\mathbb{G}}}_n:=\{(y_1,\dots ,y_{n-1},q)\in {\mathbb{C}}^n:q\in \mathbb{D},y_j={\beta }_j+{\bar{\beta }}_{n-j}q,{\beta }_j\in \mathbb{C}\text{ and }|{\beta }_j|+|{\beta }_{n-j}|<(\genfrac{}{}{0ex}{}{n}{j})\text{ for }j=1,\dots ,n-1\}.$$ We present the connection of ${\tilde{\mathbb{G}}}_n$ with the $\mu$-synthesis problem.

17 pages. To appear in "Proceedings of the Indian Academy of Sciences: Mathematical Sciences"