On R-duals and the duality principle

Ole Christensen, Diana Stoeva

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

In 2004 Casazza, Kutyniok and Lammers introduced the R-duals of sequences in a general Hilbert space. The purpose was to obtain a general version of the duality principle in Gabor analysis. It was shown that the R-duals cover the duality principle for tight Gabor frames and Gabor Riesz bases. In this paper we discuss the relationship between the R-duals and a variant, called R-duals of type III, introduced in 2014. In contrast to the original R-duals, it is known that the R-duals of type III generalize the duality principle for all Gabor frames, but we believe that a smaller and more convenient class will work as well. The purpose of the paper is to give a focussed presentation of the R-duals of type I and III that can trigger the research on this.
Original languageEnglish
Title of host publicationProceedings of the 11th International Conference on Sampling Theory and Applications (SampTA 2015)
PublisherIEEE
Publication date2015
Pages352-356
ISBN (Print)978-1-4673-7353-1
DOIs
Publication statusPublished - 2015
Event11th International Conference on Sampling Theory and Applications - Washington, United States
Duration: 25 May 201529 May 2015
Conference number: 11
http://www.american.edu/cas/mathstat/sampta2015/index.cfm

Conference

Conference11th International Conference on Sampling Theory and Applications
Number11
Country/TerritoryUnited States
CityWashington
Period25/05/201529/05/2015
Internet address

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