2012 Fiscal Year Final Research Report
Constructions of representations of solvable Lie groups and non-commutative Fourier analysis
| Project/Area Number |
21540180
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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) |
2009 – 2012
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| Keywords | 関数解析 / リー群の表現論 / ユニタリ表現 / フーリエ変換 / 非可換調和解析 / 冪零リー群 / 可解リー群 |
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| Research Abstract |
This research mainly concerns non-commutative Fourier transforms on Lie groups from the following viewpoints. For an exponent p (1＜p≦2) and its conjugate q, the L^p-Fourier transform is defined to be a bounded operator from the space of L^p-functions on the group to the L^q-space of operator fields on the unitary dual; the determination of its norm is one of the main problems of harmonic analysis. We obtained the norm for the groups defined by compact extensions of R^n. We also obtained an estimate of the norm for general connected nilpotent Lie groups. Next, we have treated the Fourier transform as a homomorphism from the C^*-algebra of the group to the C^*-algebra of bounded operator fields over the unitary dual, and began trying to analyze the image of the Fourier transform on a certain example of six dimensional solvable Lie group.
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Research Products
(15 results)
