Toronto Math Forum
APM3462016F => APM346Lectures => Chapter 8 => Topic started by: Shentao YANG on November 12, 2016, 10:05:03 PM

Why harmonic polynomial of $deg=n$ must also be homogeneous polynomial of $deg=n$?
Say, $\Delta ({x^2}  {y^2} + z) = 2  2 + 0 = 0$, but we do not count $ ({x^2}  {y^2} + z)$ as harmonic polynomial of $deg=2$.

In general NO, but we are looking at homogeneous polynomials. Obviously if a polynomial is harmonic, then all it homogeneous components are also are harmonic.