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arXiv · 1607.08392

Synthesable differentiation-invariant subspaces

Anton Baranov·Yurii Belov
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Abstract

We describe differentiation-invariant subspaces of $C^\infty(a,b)$ which admit spectral synthesis. This gives a complete answer to a question posed by A.~Aleman and B.~Korenblum. It turns out that this problem is related to a classical problem of approximation by polynomials on the real line. We will depict an intriguing connection between these problems and the theory of de Branges spaces.

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Anton Baranov, Yurii Belov. 2016-07-28. Synthesable differentiation-invariant subspaces. https://arxiv.org/abs/1607.08392

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