Frame theory in Krein spaces

Kerin 空间中的框架理论

• 批准号: 396828946
• 负责人: Professor Dr. Carsten Trunk
• 金额: --
• 依托单位: Departamento de Matemática
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2018-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/396828946?language=en
• 关键词: Frame; theory; Krein; spaces

Only a few titles of books or articles concerning frames in Hilbert spaces were published before 1991; among those is the originalpaper by Duffin and Schaeffer from 1952 and the important paper by Daubechies, Grossmann, and Meyer from 1985. Just ten years later, hundreds of papers have the word frame in the title, and today no single book can treat all the important and interesting results that have been published. Despite the fact that frame theory in Hilbert spaces is now a well-established field in applied mathematics, this is not the case for the frame theory in Krein spaces. Here most questions are still open and provide feasible and innovativemathematical research opportunities. The overall objective of the proposed project is to combine the ideas and techniques developedby both research groups (frame theory and normal projections in Krein spaces in the Argentinean group and spectral and perturbationtheory in Krein spaces in the German group) and to work jointly on the theory of frames in Krein spaces.

只有少数标题的书籍或文章有关框架在希尔伯特空间出版之前，其中是originalpaper由Duffin和Schaeffer从1952年和重要的文件Daubechies，格罗斯曼，和迈耶从1985年。仅仅十年后，数百篇论文的标题中都有框架这个词，今天没有一本书能把所有重要而有趣的结果都写出来。尽管希尔伯特空间中的框架理论现在是应用数学中一个成熟的领域，但克莱因空间中的框架理论并非如此。在这里，大多数问题仍然是开放的，并提供了可行的和创新的数学研究机会。拟议项目的总体目标是联合收割机的想法和技术开发的两个研究小组（框架理论和正常的投影在克莱因空间在阿根廷组和频谱和扰动理论在克莱因空间在德国组）和共同工作的框架理论在克莱因空间。

项目成果

On a class of non-Hermitian matrices with positive definite Schur complements

关于一类具有正定 Schur 补的非 Hermitian 矩阵

• DOI: 10.1090/proc/14412
• 发表时间: 2019
• 期刊: Proceedings of the American Mathematical Society
• 影响因子: 1
• 作者: T. Berger;J. Giribet;F. Martínez Pería;C. Trunk
• 通讯作者: C. Trunk

Spectrum of $J$-frame operators

$J$ 帧算子的频谱

• DOI: 10.7494/opmath.2018.38.5.623
• 发表时间: 2018
• 期刊: Opuscula Mathematica
• 影响因子: 1
• 作者: J. Giribet;M. Langer;L. Leben;A. Maestripieri;F. Martínez Pería;C. Trunk
• 通讯作者: C. Trunk