2022/11/04 by Ravisankar, Sivaguru, Roy, Samriddho
#32A36 32Q02 (Primary) #93D21 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2211.02689
The Friedrichs operator of a domain (in ℂn) is closely related to its Bergman projection and encodes crucial information (geometric, quadrature, potential theoretic etc.) about the domain. We show that the Friedrichs operator of a domain has rank one if the domain can be covered by a circular domain via a proper holomorphic map of finite multiplicity whose Jacobian is a homogeneous polynomial. As an application, we show that the Friedrichs operator is of rank one on the tetrablock, pentablock, and the symmetrized polydisc - domains of significance in the study of μ-synthesis in control theory.