Rank of the Friedrichs operator on domains related to $\mu$-synthesis.

Abstract :  The Friedrichs operator of a domain (in $\C^n$) is closely related to its Bergman projection and encodes crucial information about the domain. The $\mu$-synthesis problem plays an important role in Control engineering and reduces to the Nevanlinna-Pick interpolation problem in some special cases. In this talk we talk about a few domains related to $\mu$-synthesis and analyze the rank of the Friedrichs operator on these domains. Our approach is to cover each domain by some circular domain via a proper holomorphic map of finite multiplicity and use information about the rank of Friedrichs operator on circular domains. This is a joint work with Dr. Sivaguru.