The subject of harmonic analysis began with Fourier series,but soon blossomed to the Fourier transform, harmonic analysis of locally compact abelian groups, group representations, and many other variants. A more modern venue for harmonic analysis is the complex analysis of several variables.
This course will be an introduction to harmonic analysisin the complex variable context. We will treat both one-variable and several-variable questions. These will include the Bergman and Szego kernels, the Heisenberg group, the inhomogeneous Cauchy-Riemann equations, and other topics.
Any student who has passed the qualifying exams can considerhim/herself to be qualified to take this course. I will not assume that students know anything about several complex variables.
I will use material from these two books:
Function Theory of Several Complex Variables by Steven G. Krantz
Explorations in Harmonic Analysis: With Applicationsto Complex Function Theory and the Heisenberg Group by Steven G. Krantz
The first class meeting will be as scheduled by the university.At that meeting we will find a mutually agreeable time for the class.