Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: ARMEN JERBASHIAN and JOEL RESTREPO
Pages: [1] - [37]
Received Date: August 26, 2012
Submitted by:
First, some Green type potentials are introduced in the upper
half-plane, which depend on a functional parameter 
given on 
and can have any mass density near the
finite points of the real axis. These potentials possess a minimality
property in the sense that they coincide with the ordinary Green
potentials in the upper half-plane after application of some
generalization of Liouville’s fractional integration. Then, the
Riesz type descriptive representations of some Nevanlinna-Djrbashian
type classes of functions delta-subharmonic in the half-plane and
possessing there bounded Tsuji characteristics are established, where
the new potentials participate and an analogue of the Stieltjes
inversion formula is true.
potential, functional parameter, half-plane.
