I have a course project on harmonic measure and Fourier analysis.
The goal is to give a presentation on a part of harmonic measure theory which relates to Fourier analysis.
Harmonic measure is a vast body of knowledge with which I am unfamiliar.
I dwell into Garnet Harmonic measure book, but I don't see which area of the theory has connection with Fourier analysis.
Can you point to some inter connected areas?
I initialy planned to study hitting time for Brownian motion, but I think it exploit little of Fourier analysis.
I pushed my work on this subject here.
The link between harmonic measure and the hitting distribution of the Brownian motion is exhibited there.
Through Ito formula and Riesz theorem is shown that the Brownian hitting measure is the harmonic measure.
The hitting measure is shown to corresponds to the Poisson kernel in the upper half-plane, through martingale and uniqueness of Fourier transform.