一般右侧正交二维平面分割四元数波包变换

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-10-23 DOI:10.1007/s00006-023-01303-w

Hakim Monaim, Said Fahlaoui

{"title":"一般右侧正交二维平面分割四元数波包变换","authors":"Hakim Monaim, Said Fahlaoui","doi":"10.1007/s00006-023-01303-w","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we present the general right-sided quaternionic orthogonal 2D-planes split wave-packet transform that combines windowed and wavelet transforms. We derive fundamental properties: Plancherel–Parseval theorems, reconstruction formulas, and orthogonality relations, and we provide characterization range, convolutions, and some estimates. Additionally, we derive component-wise, directional and logarithmic uncertainty principles for the given transform and give a discrete formula on the square-integrable function space.\n</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"33 5","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"General Right-Sided Orthogonal 2D-Planes Split Quaternionic Wave-Packet Transform\",\"authors\":\"Hakim Monaim, Said Fahlaoui\",\"doi\":\"10.1007/s00006-023-01303-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we present the general right-sided quaternionic orthogonal 2D-planes split wave-packet transform that combines windowed and wavelet transforms. We derive fundamental properties: Plancherel–Parseval theorems, reconstruction formulas, and orthogonality relations, and we provide characterization range, convolutions, and some estimates. Additionally, we derive component-wise, directional and logarithmic uncertainty principles for the given transform and give a discrete formula on the square-integrable function space.\\n</p></div>\",\"PeriodicalId\":7330,\"journal\":{\"name\":\"Advances in Applied Clifford Algebras\",\"volume\":\"33 5\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-10-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Clifford Algebras\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00006-023-01303-w\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-023-01303-w","RegionNum":2,"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

摘要

在本文中，我们提出了一般的右侧四元数正交二维平面分裂波包变换，它结合了窗口变换和小波变换。我们导出了基本性质：Plancherel–Parseval定理、重建公式和正交关系，并提供了表征范围、卷积和一些估计。此外，我们还导出了给定变换的分量、方向和对数不确定性原理，并在平方可积函数空间上给出了一个离散公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

General Right-Sided Orthogonal 2D-Planes Split Quaternionic Wave-Packet Transform

In this paper, we present the general right-sided quaternionic orthogonal 2D-planes split wave-packet transform that combines windowed and wavelet transforms. We derive fundamental properties: Plancherel–Parseval theorems, reconstruction formulas, and orthogonality relations, and we provide characterization range, convolutions, and some estimates. Additionally, we derive component-wise, directional and logarithmic uncertainty principles for the given transform and give a discrete formula on the square-integrable function space.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.