{"title":"Quaternionic Subspace Gabor Frames and Their Duals","authors":"Yun-Zhang Li, Xiao-Li Zhang","doi":"10.1007/s00006-024-01342-x","DOIUrl":null,"url":null,"abstract":"<div><p>Due to its potential application in signal analysis and image processing, quaternionic Fourier analysis has received increasing attention. This paper addresses quaternionic subspace Gabor frames under the condition that the products of time-frequency shift parameters are rational numbers. We characterize subspace quaternionic Gabor frames in terms of quaternionic Zak transformation matrices. For an arbitrary subspace Gabor frame, we give a parametric expression of its Gabor duals of type I and type II, and characterize the uniqueness Gabor duals of type I and type II. And as an application, given a Gabor frame for the whole space <span>\\(L^{2}({\\mathbb {R}}^{2},\\,{\\mathbb {H}})\\)</span>, we give a parametric expression of its all Gabor duals, and derive its unique Gabor dual of type II. Some examples are also provided.</p></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00006-024-01342-x.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-024-01342-x","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Due to its potential application in signal analysis and image processing, quaternionic Fourier analysis has received increasing attention. This paper addresses quaternionic subspace Gabor frames under the condition that the products of time-frequency shift parameters are rational numbers. We characterize subspace quaternionic Gabor frames in terms of quaternionic Zak transformation matrices. For an arbitrary subspace Gabor frame, we give a parametric expression of its Gabor duals of type I and type II, and characterize the uniqueness Gabor duals of type I and type II. And as an application, given a Gabor frame for the whole space \(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\), we give a parametric expression of its all Gabor duals, and derive its unique Gabor dual of type II. Some examples are also provided.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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