Completely integrable systems in classical mechanics are well known to be of great interest for both theory and applications (see e.g. [1, 2] and references therein). Indeed, the possibility of analytical description of the corresponding dynamics, enables us to uncover important physical properties of the corresponding systems. The prime examples of this are the Kepler laws and numerous physica...

In this article we prove a representation formula for non-negative generalized harmonic functions with respect to subordinate Brownian motion in general open set D ⊂ R d . We also study oscillation properties of quotients Poisson integrals and that can be uniformly tamed.