# Subspaces of C-infinity invariant under the differentiation

Research output: Contribution to journal › Article

### Bibtex

@article{e396f9f6085f4dd7858e588c877dd8bd,

title = "Subspaces of C-infinity invariant under the differentiation",

abstract = "Let L be a proper differentiation invariant subspace of C-infinity (a, b) such that the restriction operator d/dx vertical bar L has a discrete spectrum Lambda (counting with multiplicities). We prove that L is spanned by functions vanishing outside some closed interval I subset of (a, b) and monomial exponentials x(k)e(lambda x) corresponding to Lambda if its density is strictly less than the critical value vertical bar I vertical bar/2 pi, and moreover, we show that the result is not necessarily true when the density of Lambda equals the critical value. This answers a question posed by the first author and B. Korenblum. Finally, if the residual part of L is trivial, then L is spanned by the monomial exponentials it contains. (C) 2015 Elsevier Inc. All rights reserved.",

keywords = "Spectral synthesis, Entire functions, Paley-Wiener spaces, Invariant, subspaces",

author = "Alexandru Aleman and Anton Baranov and Yurii Belov",

year = "2015",

doi = "10.1016/j.jfa.2015.01.002",

language = "English",

volume = "268",

pages = "2421--2439",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "8",

}