{"title":"A New Class of FBI Transforms and Applications","authors":"G. Hoepfner, R. Medrado","doi":"10.1007/s00041-024-10102-1","DOIUrl":null,"url":null,"abstract":"<p>We introduce a class of FBI transforms using weight functions (which includes the subclass of Sjöstrand’s FBI transforms used by Christ in (Commun Partial Differ Equ 22(3–4):359–379, 1997)) that is well suited when dealing with ultradifferentiable functions (see Definition 2.3) and ultradistributions (see Definition 2.15) defined by weight functions in the sense of Braun, Meise and Taylor (BMT). We show how to characterize local regularity of BMT ultradistributions using this wider class of FBI transform and, as an application, we characterize the BMT vectors (see Definition 1.2) and prove a relation between BMT local regularity and BMT vectors.</p>","PeriodicalId":15993,"journal":{"name":"Journal of Fourier Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fourier Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00041-024-10102-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce a class of FBI transforms using weight functions (which includes the subclass of Sjöstrand’s FBI transforms used by Christ in (Commun Partial Differ Equ 22(3–4):359–379, 1997)) that is well suited when dealing with ultradifferentiable functions (see Definition 2.3) and ultradistributions (see Definition 2.15) defined by weight functions in the sense of Braun, Meise and Taylor (BMT). We show how to characterize local regularity of BMT ultradistributions using this wider class of FBI transform and, as an application, we characterize the BMT vectors (see Definition 1.2) and prove a relation between BMT local regularity and BMT vectors.
我们介绍了一类使用权重函数的联邦调查局变换（其中包括克里斯特在（Comm Partial Differ Equ 22(3-4):359-379, 1997）中使用的西约斯特兰德联邦调查局变换子类），它非常适合处理超微分函数（见定义 2.3）和由布劳恩、梅斯和泰勒（BMT）意义上的权重函数定义的超分布（见定义 2.15）。我们展示了如何利用这一类更广泛的联邦调查局变换来表征 BMT 超分布的局部正则性，作为应用，我们表征了 BMT 向量（见定义 1.2），并证明了 BMT 局部正则性与 BMT 向量之间的关系。
期刊介绍：
The Journal of Fourier Analysis and Applications will publish results in Fourier analysis, as well as applicable mathematics having a significant Fourier analytic component. Appropriate manuscripts at the highest research level will be accepted for publication. Because of the extensive, intricate, and fundamental relationship between Fourier analysis and so many other subjects, selected and readable surveys will also be published. These surveys will include historical articles, research tutorials, and expositions of specific topics.
TheJournal of Fourier Analysis and Applications will provide a perspective and means for centralizing and disseminating new information from the vantage point of Fourier analysis. The breadth of Fourier analysis and diversity of its applicability require that each paper should contain a clear and motivated introduction, which is accessible to all of our readers.
Areas of applications include the following:
antenna theory * crystallography * fast algorithms * Gabor theory and applications * image processing * number theory * optics * partial differential equations * prediction theory * radar applications * sampling theory * spectral estimation * speech processing * stochastic processes * time-frequency analysis * time series * tomography * turbulence * uncertainty principles * wavelet theory and applications
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