Effectiveness of transposed inverse sets in faber regions - J. A. Adepoju; M. Nassif (International Journal of Mathematics and Mathematical Sciences)
The effectiveness properties, in Faber regions, of the transposed inverse of a given basic set of polynominals, are investigated in the present paper. A certain inevitable normalizing substitution, is first formulated, to be undergone by the given set to ensure the existence of the transposed inverse in the Faber region. The first main result of the present work (Theorem 2.1), on the one hand, provides a lower bound of the class of functions for which the normalized transposed inverse set is effective in the Faber region. On the other hand, the second main result (Theorem 5.2) asserts the fact that the normalized transposed inverse set of a simple set of polynomials, which is effective in a Faber region, should not necessarily be effective there.