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Bohr sets for multiplier algebras of complete Pick spaces
Abstract
We reexamine F. Wiener's classical proof that the Bohr radius of H∞ is 1/3. We replace H∞ by the multiplier algebras of complete Pick spaces and describe the Bohr set for a wide class of such algebras. In particular, we show that the Bohr set of the multiplier algebra of the Drury--Arveson space H2d is the closed ℓ2-ball of radius 1/3. Other cases covered by our description of Bohr sets include Dirichlet-type spaces of analytic functions in the unit disc and a class of Hilbert spaces of ordinary Dirichlet series, studied earlier by McCarthy and Shalit.
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BibTeX
@misc{brevig2026bohr,
title = {{Bohr sets for multiplier algebras of complete Pick spaces}},
author = {Ole Fredrik Brevig and Kristian Seip and Ilya Zlotnikov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26395},
eprint = {2609.26395},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26395},
}
RIS
TY - UNPB
TI - Bohr sets for multiplier algebras of complete Pick spaces
AU - Ole Fredrik Brevig
AU - Kristian Seip
AU - Ilya Zlotnikov
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26395
UR - https://arxiv.org/abs/2609.26395
AB - We reexamine F. Wiener's classical proof that the Bohr radius of H^∞ is 1/3. We replace H^∞ by the multiplier algebras of complete Pick spaces and describe the Bohr set for a wide class of such algebras. In particular, we show that the Bohr set of the multiplier algebra of the Drury--Arveson space H^2_d is the closed ℓ^2-ball of radius 1/3. Other cases covered by our description of Bohr sets include Dirichlet-type spaces of analytic functions in the unit disc and a class of Hilbert spaces of ordinary Dirichlet series, studied earlier by McCarthy and Shalit.
ER -