No abstract

No abstract

No abstract

A harmonic function defined in a cone and vanishing on the boundary is expanded into an infinite sum of certain fundamental harmonic functions. The growth conditions under which it is reduced to a finite sum of them are discussed.

We shall give two criteria of Wiener type which characterize minimally thin sets and rarefied sets in a cylinder. We shall also show that a positive superharmonic function on a cylinder behaves regularly outside a rarefied set in a cylinder.