Subspaces of Cinfinity invariant under the differentiation
(2015) In Journal of Functional Analysis 268(8). p.24212439 Abstract
 Let L be a proper differentiation invariant subspace of Cinfinity (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 Cinfinity (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:
http://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, PaleyWiener spaces, Invariant, subspaces
 in
 Journal of Functional Analysis
 volume
 268
 issue
 8
 pages
 2421  2439
 publisher
 Elsevier
 external identifiers

 wos:000351807700012
 scopus:84924140534
 ISSN
 00221236
 DOI
 10.1016/j.jfa.2015.01.002
 language
 English
 LU publication?
 yes
 id
 e396f9f6085f4dd7858e588c877dd8bd (old id 5277723)
 date added to LUP
 20150424 09:15:42
 date last changed
 20180107 07:24:19
@article{e396f9f6085f4dd7858e588c877dd8bd, abstract = {Let L be a proper differentiation invariant subspace of Cinfinity (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 = {00221236}, keyword = {Spectral synthesis,Entire functions,PaleyWiener spaces,Invariant,subspaces}, language = {eng}, number = {8}, pages = {24212439}, publisher = {Elsevier}, series = {Journal of Functional Analysis}, title = {Subspaces of Cinfinity invariant under the differentiation}, url = {http://dx.doi.org/10.1016/j.jfa.2015.01.002}, volume = {268}, year = {2015}, }