Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.