The closedness of shift invariant subspaces in [Formula: see text]

In this paper, we consider the closedness of shift invariant subspaces in [Formula: see text] . We first define the shift invariant subspaces generated by the shifts of finite functions in [Formula: see text] . Then we give some necessary and sufficient conditions for the shift invariant subspaces i...

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Detalles Bibliográficos
Autor principal: Zhang, Qingyue
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061598/
https://www.ncbi.nlm.nih.gov/pubmed/30137894
http://dx.doi.org/10.1186/s13660-018-1755-2
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author Zhang, Qingyue
author_facet Zhang, Qingyue
author_sort Zhang, Qingyue
collection PubMed
description In this paper, we consider the closedness of shift invariant subspaces in [Formula: see text] . We first define the shift invariant subspaces generated by the shifts of finite functions in [Formula: see text] . Then we give some necessary and sufficient conditions for the shift invariant subspaces in [Formula: see text] to be closed. Our results improve some known results in (Aldroubi et al. in J. Fourier Anal. Appl. 7:1–21, 2001).
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spelling pubmed-60615982018-08-09 The closedness of shift invariant subspaces in [Formula: see text] Zhang, Qingyue J Inequal Appl Research In this paper, we consider the closedness of shift invariant subspaces in [Formula: see text] . We first define the shift invariant subspaces generated by the shifts of finite functions in [Formula: see text] . Then we give some necessary and sufficient conditions for the shift invariant subspaces in [Formula: see text] to be closed. Our results improve some known results in (Aldroubi et al. in J. Fourier Anal. Appl. 7:1–21, 2001). Springer International Publishing 2018-07-06 2018 /pmc/articles/PMC6061598/ /pubmed/30137894 http://dx.doi.org/10.1186/s13660-018-1755-2 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Zhang, Qingyue
The closedness of shift invariant subspaces in [Formula: see text]
title The closedness of shift invariant subspaces in [Formula: see text]
title_full The closedness of shift invariant subspaces in [Formula: see text]
title_fullStr The closedness of shift invariant subspaces in [Formula: see text]
title_full_unstemmed The closedness of shift invariant subspaces in [Formula: see text]
title_short The closedness of shift invariant subspaces in [Formula: see text]
title_sort closedness of shift invariant subspaces in [formula: see text]
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6061598/
https://www.ncbi.nlm.nih.gov/pubmed/30137894
http://dx.doi.org/10.1186/s13660-018-1755-2
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