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Subspaces of C-infinity invariant under the differentiation

På svenska

Author

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.

Publishing year

2015

Language

English

Pages

2421-2439

Publication/Series

Journal of Functional Analysis

Volume

268

Issue

8

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Spectral synthesis
  • Entire functions
  • Paley-Wiener spaces
  • Invariant
  • subspaces

Status

Published

ISBN/ISSN/Other

  • ISSN: 0022-1236