Explicit bounds of complex exponential frames

Explicit bounds of complex exponential frames

<p/> <p>We discuss the stability of complex exponential frames <inline-formula><graphic file="1029-242X-2006-38173-i1.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-38173-i2.gif"/></inline-formula>, <inl...

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Main Authors: Boivin Andr&#233;, Zhong Hualiang, Peters Terry M
Format: Article
Language:English
Published: SpringerOpen 2006-01-01
Series:Journal of Inequalities and Applications
Online Access:http://www.journalofinequalitiesandapplications.com/content/2006/38173
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spelling doaj-720a9133849f423f9a543ebd042a6e532020-11-25T00:51:32ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2006-01-012006138173Explicit bounds of complex exponential framesBoivin Andr&#233;Zhong HualiangPeters Terry M<p/> <p>We discuss the stability of complex exponential frames <inline-formula><graphic file="1029-242X-2006-38173-i1.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-38173-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-38173-i3.gif"/></inline-formula>. Specifically, we improve the <inline-formula><graphic file="1029-242X-2006-38173-i4.gif"/></inline-formula>-theorem and obtain explicit upper and lower bounds for some complex exponential frames perturbed along the real and imaginary axes, respectively. Two examples are given to show that the bounds are best possible. In addition, the growth of the entire functions of exponential type <inline-formula><graphic file="1029-242X-2006-38173-i5.gif"/></inline-formula> <inline-formula><graphic file="1029-242X-2006-38173-i6.gif"/></inline-formula> on the integer sequence is estimated.</p>http://www.journalofinequalitiesandapplications.com/content/2006/38173
collection DOAJ
language English
format Article
sources DOAJ
author Boivin Andr&#233;
Zhong Hualiang
Peters Terry M
spellingShingle Boivin Andr&#233;
Zhong Hualiang
Peters Terry M
Explicit bounds of complex exponential frames
Journal of Inequalities and Applications
author_facet Boivin Andr&#233;
Zhong Hualiang
Peters Terry M
author_sort Boivin Andr&#233;
title Explicit bounds of complex exponential frames
title_short Explicit bounds of complex exponential frames
title_full Explicit bounds of complex exponential frames
title_fullStr Explicit bounds of complex exponential frames
title_full_unstemmed Explicit bounds of complex exponential frames
title_sort explicit bounds of complex exponential frames
publisher SpringerOpen
series Journal of Inequalities and Applications
issn 1025-5834
1029-242X
publishDate 2006-01-01
description <p/> <p>We discuss the stability of complex exponential frames <inline-formula><graphic file="1029-242X-2006-38173-i1.gif"/></inline-formula> in <inline-formula><graphic file="1029-242X-2006-38173-i2.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-38173-i3.gif"/></inline-formula>. Specifically, we improve the <inline-formula><graphic file="1029-242X-2006-38173-i4.gif"/></inline-formula>-theorem and obtain explicit upper and lower bounds for some complex exponential frames perturbed along the real and imaginary axes, respectively. Two examples are given to show that the bounds are best possible. In addition, the growth of the entire functions of exponential type <inline-formula><graphic file="1029-242X-2006-38173-i5.gif"/></inline-formula> <inline-formula><graphic file="1029-242X-2006-38173-i6.gif"/></inline-formula> on the integer sequence is estimated.</p>
url http://www.journalofinequalitiesandapplications.com/content/2006/38173
work_keys_str_mv AT boivinandr233 explicitboundsofcomplexexponentialframes
AT zhonghualiang explicitboundsofcomplexexponentialframes
AT petersterrym explicitboundsofcomplexexponentialframes
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