Park City Mathematics Institute
Undergraduate Summer School 2018
Introduction to Harmonic Analysis
- The function is harmonic for each , where is the Poisson kernel for the ball.
- (Symmetry Lemma) For any and , .
- (Harnack’s inequality) If is a positive harmonic function on , then
- (Hopf Lemma) If is a nonconstant harmonic function on and attains its maximum at , there exists such that for any
- If is harmonic on and its normal derivative is 0 everywhere on , then is constant.
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