Abstract
We study the class of the Riesz subsets of abelian discrete groups, that is, the sets for which the F. and M. Riesz theorem extends. We show that the “classical” tools of the theory — Riesz projections, localization in the Bohr sense, products — are leading to Riesz sets which are satisfying nice additional properties, e.g., the Mooney-Havin result extends to this class. We give an alternative proof of a result of A. B. Alexandrov, and we improve a construction of H. P. Rosenthal. The connection is made between this class and theM-structure theory. We show a result of convergence at the boundary for holomorphic functions on the polydisc. The Bourgain-Davis result on convergence of analytic martingales is improved.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.