Subspaces of C-infinity invariant under the differentiation

Summary, in English

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.

• Författare: Alexandru Aleman; Anton Baranov; Yurii Belov
• Avdelning/ar: Matematik (naturvetenskapliga fakulteten)
• Publiceringsår: 2015
• Språk: Engelska
• Sidor: 2421-2439
• Publikation/Tidskrift/Serie: Journal of Functional Analysis
• Volym: 268
• Issue: 8
• Länkar: http://dx.doi.org/10.1016/j.jfa.2015.01.002
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: Spectral synthesis; Entire functions; Paley-Wiener spaces; Invariant; subspaces
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0022-1236