Group-theoretical research of eigenvalue problems and its applications

特征值问题的群论研究及其应用

• 批准号: 60460006
• 负责人: YOSHIZAWA Hisaaki
• 金额: $ 4.35万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-60460006/
• 关键词: eigenvalue problem; Fourier transform; unitary representation; hypergroup; Hecke operater; Schrodinger operater; 逆問題

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.

1. 摘要群论和特征值问题在数学的许多领域中都具有重要的意义，并且彼此密切相关，本文用代数理论和泛函分析的方法研究了这两个问题。在本项目的第一阶段，用历史的观点对这一领域的许多已知成果进行了积累、比较和深化，然后从这些调查中得出了重要的新结果。1985年和1986年，在泛函分析、李群、数论、微分方程、概率论和数学物理等多个领域的研究都参加了该项目的研究，并取得了许多成果。在开展调查的过程中，不断与国内外其他大学的研究人员进行讨论和信息交流。通过研究，从历史的角度获得了许多重要的文献和知识。在本项目跨学科研究成果的积累下，正在形成未来一些重要研究的希望病菌。

项目成果

Yoshida,H.: Algebraic and Topological Theories. 197-238 (1985)

Yoshida,H.：代数和拓扑理论。

Kotani, S.: "Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrodinger operators." Ann. Inst. Henri Poincare. 42. 383-406 (1985)

Kotani, S.：“对于某些一维随机但确定性的薛定谔算子来说，缺乏绝对连续的谱。”

Nomura, T.: "Fourier transform of a space of holomorphic discrete series." Proc. Japan Acad.61. 133-136 (1985)

Nomura, T.：“全纯离散级数空间的傅里叶变换。”

Kotani,S.: rs.Ann.Inst.Henri Poincar【e!´】. 42. 383-406 (1985)

Kotani, S.：rs.Ann.Inst.Henri Poincar [e!´]。 42. 383-406 (1985)。

Hirai, T.: "Unitary representations of supergroups." Math. Physics Studies. 8. 16-67 (1986)

Hirai, T.：“超群的统一表示。”