Properties of spectra of differentiation invariant subspace in the Schwarz space

2 Jul 2021, 10:45


Natalia Abuzyarova (Bashkir State University)


Let $E$ be the Schwartz space of infinitely differentiable functions on the real line. We consider its closed differentiation invariant subspace $W$ with discrete spectrum $L$ which is weakly synthesable. It means that $W$ is the closed span of its residual subspace and the set $\rm{Exp} W$ of all exponential monomials contained in $W$. Among all weakly synthesable subspaces $W$, there are nice ones which equal the direct (algebraical and topological) sum of the residual part of $W$ and the closed span of $\rm{Exp} W$. Does given weakly synthesable subspace $W$ equal such a direct sum or not? The answer is obtained in terms of characteristics and (or) properties of the spectrum $L$.

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Natalia Abuzyarova (Bashkir State University)

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