Abstract:
Recently, was developed a new theory of the Jost function, within
which, it was split in two terms involving on one side, singlevalued
analytic functions of the energy, and on the other, factors
responsible for the existence of the branching-points. For the
single-valued part of the Jost function, a procedure for the powerseries
expansion around an arbitrary point on the energy plane
was suggested. However, this theory lacks a rigorous proof that
these parts are entire functions of the energy. It also gives an
intuitive (not rigorous) derivation of the domain where they are
entire. In the present study, we ll this gap by using a method
derived from the method of successive approximations.
