The classical Mittag-Leffler theorem on meromorphic functions is extended to the case of functions and hyperfunctions belonging to the kernels of linear partial differential operators with constant coefficients.
This paper shows that some characterizations of the harmonic majorization of the Martin function for domains having smooth boundaries also hold for cones.
The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator on is proved. In this note there is shown that in the cases , no other transforms of this kind exist and for case , all such transforms are described.
We construct bounded domains D not equal to a ball in n ≥ 3 dimensional Euclidean space, Rn, for which ∂D is homeomorphic to a sphere under a quasiconformal mapping of Rn and such that n - 1 dimensional Hausdorff measure equals harmonic measure on ∂D.
The main result of the present paper is : every separately-subharmonic function , which is harmonic in , can be represented locally as a sum two functions, , where is subharmonic and is harmonic in , subharmonic in and harmonic in outside of some nowhere dense set .