It is well-known fact that if you average a harmonic function over the area of a sphere, you get the value of the harmonic function evaluated at the sphere's center. (Let's restrict the dimension to 3.)
But as we can understand this averaging is done over solid angle, I was motivated to generalize it to some point other than the center of the sphere.
Does the average over solid angle with respect to the pont other than the center of the sphere have any meaning?
(sorry for lack of any rigorous equations. It's hard to type TEX codes on mobile device, so let me edit it later...)