Park City Mathematics Institute
Undergraduate Summer School 2018
Introduction to Harmonic Analysis
- Let be orthogonal.
- If is harmonic, then is also harmonic.
- If is a translation and is harmonic, then is harmonic.
- Use polar coordinates to verify
- Use (3.1) to prove , for any .
- Use spherical coordinates and the previous result to prove , where is the Gamma function.
- Use the divergence theorem to prove Green’s identity. (Hint: Consider .)
- The function is harmonic in .
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