Scalability of Generalized Frames for Operators

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-16 DOI:10.1155/2024/8358987

Varinder Kumar, Sapna Malhotra, Nikhil Khanna

引用次数: 0

Abstract

In this paper, the Parseval --frames are constructed from a given --frame by scaling the elements of the --frame with the help of diagonal operators, and these frames are named scalable --frames. Also, we prove some properties of scalable --frames and construct new scalable --frames from a given --frame. The necessary and sufficient conditions for a --frame to be scalable are given. Further, equivalent conditions for the scalability of --frames and the -frames induced by --frames are obtained. Finally, it is shown that the direct sum of two scalable --frames is again a scalable --frame for some suitable bounded linear operator .

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算子广义框架的可扩展性

在本文中，我们借助对角线算子缩放--框架中的元素，从给定的--框架中构造出 Parseval--框架，这些框架被命名为可缩放--框架。此外，我们还证明了可缩放--框架的一些属性，并从给定的--框架构造了新的可缩放--框架。我们给出了可扩展--框架的必要条件和充分条件。此外，还得到了--帧和由--帧诱导的--帧的可扩展性的等价条件。最后，证明了对于某些合适的有界线性算子，两个可扩展--帧的直接和也是一个可扩展--帧。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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.