Factorization of Matrix Functions and Singular Integral Operators
Factorization of Matrix Functions and Singular Integral Operators
复制标题
DOI：
10.1007/978-3-0348-5492-4
复制
发表时间：
1980
期刊：
影响因子：
4.5
通讯作者：
K. Clancey;I. Gohberg
中科院分区：
文献类型：
--
作者：
K. Clancey;I. Gohberg
几年阿加，作者开始了一个关于一维奇异积分方程系统理论的书的项目，该项目计划作为作者之一和N. Ya. Krupnik~~关于纯量方程。这一组笔记开始作为一章处理问题的因式分解矩阵功能与appli阳离子系统的奇异积分方程。系统地研究这一章，沿着这条路加入新的观点、新的证明和结果，我们终于看到，与因子分解有关的材料是独立的，我们决定把这一章作为单独的卷出版。事实上，由于最近的活动，材料的数量相当大，我们很快就了解到，我们无法完全详细地涵盖所有结果。我们试图包括各种有代表性的方法，技术，结果和应用。除了目前的工作暴露的结果从俄罗斯文学从未出现在英语翻译。我们还决定反映最近的一些结果，使有趣的矩阵函数分解和系统理论之间的联系。这个领域仍然非常活跃，许多结果和联系仍然没有很好地理解。这些说明应被视为进一步发展的垫脚石。作者希望有一天他们会回来完成他们最初的计划。
A few years aga the authors started a project of a book on the theory of systems of one-dimensional singular integral equa tions which was planned as a continuation of the monograph by one of the authors and N. Ya. Krupnik~~ concerning scalar equa tions. This set of notes was initiated as a chapter dealing with problems of factorization of matrix functions vis-a-vis appli cations to systems of singular integral equations. Working systematically onthischapter and adding along the way new points of view, new proofs and results, we finally saw that the material connected with factorizations is of independent interest and we decided to publish this chapter as aseparate volume. In fact, because of recent activity, the amount of material was quite large and we quickly learned that we cannot cover all of the results in complete detail. We have tried to include a represen tative variety of all kinds of methods, techniques, results and applications. Apart of the current work exposes results from the Russian literature which have never appeared in English translation. We have also decided to reflect some of the recent results which make interesting connections between factorization of matrix functions and systems theory. The field remains very active and many results and connec tions are still not weIl understood. These notes should be viewed as a stepping stone to further development. The authors hope that sometime they will return to complete their original plan.