Group-theoretical research of eigenvalue problems and its applications

1.群论与特征值问题是数学中的两个重要问题，它们在数学的许多领域都有着密切的联系，本文用代数论和泛函分析的方法来研究这两个问题。在本项目的第一阶段，积累、比较和深化了该领域的许多已知成果，并从这些研究中获得了重要的新成果.在1985年和1986年，在几个领域，特别是在泛函分析，李群，数论，微分方程，概率和数学物理领域的研究，参加了这个研究项目，并取得了许多成果.在进行调查时，与国内外其他大学的研究人员不断进行讨论和交流信息。从历史的角度进行研究，获得了许多重要的文献和认识.积累在目前的跨学科研究项目中取得的成果，正在形成一些重要的未来研究的希望萌芽。

1. The general purpose The group theory and the eigenvalue problem, which are important in many fields of mathematics and closely related each other, are both investigated by the methods of theory of algebras and functional analysis. In the first stage of the present project, many of the known results in this field were accumulated, compared, and also deepend with historical viewpoint, and afterwards from such investigations important new results were derived.2. In 1985 and 1986, researches in several fields, in particular, in the fields of functional analysis, Lie groups, number theory, differential equations, probability and mathematical physics, took parts in this research project and many results have been obtained.3. In carrying out investigations, discussion and exchange of information were constantly maintained with researchers both in other domestic unversities and abroad.4. Many important documents and knowledge were obtained by the study from the historical viewpoints.5. Accumulating the results obtained in the present project of interdisciplinary investigation, hopeful germs of some important future research are being formed.