Amenable locally compact groups and A_p(G)

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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: