Some Remarks on the Algebra of Bounded Dirichlet Series
Brian Maurizi, Herve Queffelec

TL;DR
This paper investigates the algebraic structure of bounded Dirichlet series, demonstrating the failure of the Corona theorem in this context and refining the Hille-Bohnenblust theorem using probabilistic and deterministic methods.
Contribution
It shows the Corona theorem does not hold for bounded Dirichlet series and provides refined versions of the Hille-Bohnenblust theorem with detailed proofs.
Findings
Corona theorem is false in this setting
Right half-plane is not dense in the maximal ideal space
Refined Hille-Bohnenblust theorem with probabilistic and deterministic proofs
Abstract
We examine the algebra of all Dirichlet Series bounded on the right half plane. We consider the analogue of the Corona theorem in this setting, and show that it is false, i.e. the right half-plane is not dense in the maximal ideal space. We also prove some refinements of the Hille-Bohnenblust theorem, where both probabilistic and deterministic devices are used, and we show how the proof is carried out for each.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Topics in Algebra · Advanced Operator Algebra Research
