At the foundation of harmonic analysis are the well-known principles that a geometric space may be studied though its space of functions, and that the analysis of these functions is simplified by taking into account the symmetries of the space.Over the past 60 years, considerable developments have occurred in the global analysis on spaces acted upon by real reductive groups as a generalization of Fourier analysis.
These lectures will focus on several fundamental aspects of this study in which irreducible tempered representations act as gbuilding blocksh of Langlandsf classification theory. Topics will include: real spherical manifolds, the representation theory of real reductive groups, branching laws, tempered homogeneous spaces, examples and applications of tempered varieties.
© Toshiyuki Kobayashi