X-Nico

unusual facts about harmonic function



Newtonian potential

It is named for Isaac Newton, who first discovered it and proved that it was a harmonic function in the special case of three variables, where it served as the fundamental gravitational potential in Newton's law of universal gravitation.

Radó–Kneser–Choquet theorem

In mathematics, the Radó–Kneser–Choquet theorem, named after Tibor Radó, Hellmuth Kneser and Gustave Choquet, states that the Poisson integral of a homeomorphism of the unit circle is a harmonic diffeomorphism of the open unit disk.


see also

Gabor filter

Because of the multiplication-convolution property (Convolution theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function and the Fourier transform of the Gaussian function.

Jensen's formula

which is the Poisson formula for the harmonic function f(z)|.