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


This course will be an introduction to harmonic analysis

in 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 consider

him/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 Applications

to 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.