The Friedrichs operator and circular domains
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- by Sivaguru Ravisankar and Samriddho Roy;
- Proc. Amer. Math. Soc. 152 (2024), 1587-1597
- DOI: https://doi.org/10.1090/proc/16606
- Published electronically: February 9, 2024
- HTML | PDF
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.References
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Bibliographic Information
- Sivaguru Ravisankar
- Affiliation: Tata Institute of Fundamental Research Centre for Applicable Mathematics, Bengaluru 560065, India
- MR Author ID: 1054138
- ORCID: 0000-0003-1857-9260
- Email: sivaguru@tifrbng.res.in
- Samriddho Roy
- Affiliation: Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Delhi Centre, New Delhi 110016, India
- MR Author ID: 1253074
- Email: samriddhoroy@gmail.com
- Received by editor(s): November 4, 2022
- Received by editor(s) in revised form: July 7, 2023, and July 9, 2023
- Published electronically: February 9, 2024
- Additional Notes: The second author was partially supported by an INSPIRE Faculty Fellowship grant DST/INSPIRE/04/2016/000237 of Professor Shyam Sundar Ghoshal.
- Communicated by: Harold P. Boas
- © Copyright 2024 by the authors
- Journal: Proc. Amer. Math. Soc. 152 (2024), 1587-1597
- MSC (2020): Primary 32A36, 32Q02; Secondary 93D21
- DOI: https://doi.org/10.1090/proc/16606
- MathSciNet review: 4709228