The Friedrichs Operator and Circular Domains

Sivaguru Ravisankar; Samriddho Roy

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arXiv · 2211.02689

The Friedrichs Operator and Circular Domains

Sivaguru Ravisankar·Samriddho Roy

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Abstract

The Friedrichs operator of a domain (in $\mathbb{C}^n$) 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 $\mu$-synthesis in control theory.

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Sivaguru Ravisankar, Samriddho Roy. 2022-11-04. The Friedrichs Operator and Circular Domains. https://arxiv.org/abs/2211.02689

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