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arXiv · 2606.09807

A pathological de Branges-Rovnyak space

Thomas Ransford
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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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Thomas Ransford. 2026-06-08. A pathological de Branges-Rovnyak space. https://arxiv.org/abs/2606.09807

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