Non-commutative Fourier analysis on solvable Lie groups and its applications in analysis on homogeneous spaces
| Project/Area Number |
25400115
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tottori University |
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Principal Investigator |
Inoue Junko 鳥取大学, 大学教育支援機構, 准教授 (40243886)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | フーリエ変換 / 複素解析的誘導表現 / 可解リー群 / ユニタリ表現 / 軌道法 / 非可換調和解析 / 表現論 / 国際研究者交流 / フランス：チュニジア / 軌道の方法 |
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| Outline of Final Research Achievements |
Concerning non-commutative Fourier transforms, we studied two examples of exponential solvable Lie groups; for them we described the images of their C*-algebras by the Fourier transform in terms of the orbit method. For the norm of the Lp-Fourier transform (1<p<2), we treated a semi-direct product group of a unimodular type I Lie group N and a compact group acting on N, and we obtained an estimate of the norm of its Lp-Fourier transform by using that of N.
For holomorphically induced representations, we studied a semi-direct product group G of a vector group Rn and R acting on Rn. Assuming that there is a complex one dimensional subalgebra h such that the space h+h~, where h~ is the complex conjugate of h, generates the complexification of the Lie algebra of G and that G satisfies some technical conditions, we obtained a non-zero representation holomorphically induced from h, and its decomposition into a direct integral of irreducible representations.
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Report
(5 results)
Research Products
(14 results)
