An Overview of Dualities in Non-commutative Harmonic Analysis
摘要
The aim of this mini-course is to give an overview of duality tools of the non-commutative harmonic analysis. By volume limitations, it cannot be complete, but tries to be as wide as possible and accessible to starting Ph.D. students. I start with the unitary dual of a locally compact group, then discuss the Plancherel measure on it and disintegration results. The following outlines of symmetric spaces, non-commutative \(L^p\) spaces and quantum groups are very brief, but allow to present several results on Fourier multipliers in non-commutative settings.