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Subspaces of C-infinity invariant under the differentiation

Aleman, Alexandru LU ; Baranov, Anton and Belov, Yurii (2015) In Journal of Functional Analysis 268(8). p.2421-2439
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Spectral synthesis, Entire functions, Paley-Wiener spaces, Invariant, subspaces
in
Journal of Functional Analysis
volume
268
issue
8
pages
2421 - 2439
publisher
Elsevier
external identifiers
  • wos:000351807700012
  • scopus:84924140534
ISSN
0022-1236
DOI
10.1016/j.jfa.2015.01.002
language
English
LU publication?
yes
id
e396f9f6-085f-4dd7-858e-588c877dd8bd (old id 5277723)
date added to LUP
2015-04-24 09:15:42
date last changed
2017-11-05 04:03:18
@article{e396f9f6-085f-4dd7-858e-588c877dd8bd,
  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.},
  author       = {Aleman, Alexandru and Baranov, Anton and Belov, Yurii},
  issn         = {0022-1236},
  keyword      = {Spectral synthesis,Entire functions,Paley-Wiener spaces,Invariant,subspaces},
  language     = {eng},
  number       = {8},
  pages        = {2421--2439},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Subspaces of C-infinity invariant under the differentiation},
  url          = {http://dx.doi.org/10.1016/j.jfa.2015.01.002},
  volume       = {268},
  year         = {2015},
}