Subspaces of C-infinity invariant under the differentiation
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5277723
- author
- Aleman, Alexandru LU ; Baranov, Anton and Belov, Yurii
- organization
- publishing date
- 2015
- 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
- 2016-04-01 13:53:06
- date last changed
- 2022-03-06 08:17:52
@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}},
keywords = {{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}},
doi = {{10.1016/j.jfa.2015.01.002}},
volume = {{268}},
year = {{2015}},
}