We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.
We complement a previous result concerning a converse of the mean-value property for smooth superharmonic functions. The case of harmonic functions was treated by Kuran and an improvement was given by Armitage and Goldstein.
In this paper we study some potential theoretical properties of solutions and super-solutions of some PDE systems (S) of type , , on a domain of , where and are suitable measures on , and , are two second order linear differential elliptic operators on with coefficients of class . We also obtain the integral representation of the nonnegative solutions and supersolutions of the system (S) by means of the Green kernels and Martin boundaries associated with and , and a convergence...