I am sorry if this questions turns out to be "too broad" or "unclear", since I really know very little about the Langlands program. What I am wondering is that what kind of harmonic analysis is used in the the Langlands program.
Is it just Fourier series/transforms, or classical Fourier analysis, or abstract harmonic analysis? Or some "harmonic analysis" developed just for Langlands program theorists that are quite different from that of PDE theorists?
What are good references/online notes etc. for the harmonic analysis designated for the Langlands program?