Non-commutative Fourier analysis on solvable Lie groups and its applications in analysis on homogeneous spaces

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400115
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tottori University
• Principal Investigator: Inoue Junko 鳥取大学, 大学教育支援機構, 准教授 (40243886)
• Project Period (FY): 2013-04-01 – 2017-03-31
• 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

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.

Free Research Field

表現論