Frame theory in Krein spaces

1991年以前出版的关于希尔伯特空间框架的书籍或文章很少；其中包括Duffin和Schaeffer在1952年发表的原创论文，以及Daubechies、Grossmann和Meyer在1985年发表的重要论文。仅仅十年后，数百篇论文的标题中都有“框架”这个词，而今天，没有一本书可以涵盖所有已经发表的重要和有趣的结果。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，但克林空间中的框架理论却不是这样。这里的大多数问题仍然是开放的，并提供了可行和创新的数学研究机会。拟议项目的总体目标是结合两个研究小组开发的思想和技术（阿根廷组的Krein空间中的框架理论和正投影，德国组的Krein空间中的谱和摄动理论），并共同研究Krein空间中的框架理论。

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.