English

Synthesable differentiation-invariant subspaces

Complex Variables 2018-04-03 v2

Abstract

We describe differentiation-invariant subspaces of C(a,b)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.

Keywords

Cite

@article{arxiv.1607.08392,
  title  = {Synthesable differentiation-invariant subspaces},
  author = {Anton Baranov and Yurii Belov},
  journal= {arXiv preprint arXiv:1607.08392},
  year   = {2018}
}

Comments

27 pages, The results of the paper are substantially improved and a complete description of synthesable spectra is obtained

R2 v1 2026-06-22T15:06:30.221Z