Amenable locally compact groups and A_p(G)

我的研究兴趣是使用算子代数和群表示的强大工具来研究调和分析和Banach代数。本文的主要研究对象是局部紧拓扑群G、傅立叶代数A(G)和B(G)、Figa-Talamanca-Herz代数A_p(G)和更一般的Banach代数W_p(G)，以及与G有关的一些其他Banach代数。这些数学对象本质上既是代数的又是拓扑的，被许多数学家广泛研究，如Antoine Derighetti，Brian Forrest，Ed。格拉尼耶，刘炽平，帕特森，阮中金和罗森布拉特。这些对象不仅在理论数学领域很重要，而且对物理学家、统计学家和社会科学家也非常有用。在我计划解决的一些问题中有以下几个：

My research interest is in harmonic analysis and Banach algebras using powerful tools from operator algebras and group representations. The main objects of my study are the locally compact topological groups G, the Fourier and Fourier-Stieltjes algebras A(G) and B(G), the Figa-Talamanca-Herz algebra A_p(G) and the more general Banach algebra W_p(G), as well as some other Banach algebras associated to G. These mathematical objects are both algebraic and topological in nature, and are widely studied by many mathematicians such as Antoine Derighetti, Brian Forrest, Ed. Granirer, Anthony Lau, Alan Paterson, Zhong-Jin Ruan and Joseph Rosenblatt. These objects are not only important in the area of theoretical mathematics, but also very useful to physicists, statisticians and social scientists. Among some of the problems that I plan to work on are the following: