PreprintCC BY 4.0arXiv
A pathological de Branges-Rovnyak space
Abstract
We construct a de Branges-Rovnyak space containing the polynomials as a dense subspace, together with a function in the space that lies outside the closed linear span of its Taylor partial sums. The space has the further property that the monomials are bounded in norm. The construction is carried out by reducing it to an elementary problem about series, which we then solve.
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BibTeX
@misc{ransford2026pathological,
title = {{A pathological de Branges-Rovnyak space}},
author = {Thomas Ransford},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.09807},
eprint = {2606.09807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.09807},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A pathological de Branges-Rovnyak space
AU - Thomas Ransford
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2606.09807
UR - https://arxiv.org/abs/2606.09807
AB - We construct a de Branges-Rovnyak space containing the polynomials as a dense subspace, together with a function in the space that lies outside the closed linear span of its Taylor partial sums. The space has the further property that the monomials are bounded in norm. The construction is carried out by reducing it to an elementary problem about series, which we then solve.
ER -