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Effectiveness of transposed inverse sets in Faber regions. (English) Zbl 0544.30033
The authors investigate the effectiveness of the transposed inverse of a given basic set of polynomials in Faber regions. To ensure the existence of the transposed inverse in Faber region, a ”normalizing substitution” on the given set is first introduced. The first main result gives a lower bound of the class of functions for which the normalized transposed inverse set is effective in the appropriate Faber region, while the second demonstrates the fact that a simple set of polynomials may be effective in the Faber region while its normalized transposed inverse set may not be effective there.
30E10 Approximation in the complex plane
41A10 Approximation by polynomials
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