Group-theoretical research of eigenvalue problems and its applications

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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.