Synthesable differentiation-invariant subspaces

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.

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

References in corpus (1)

• Canonical systems and de Branges spaces