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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.
MSC:
30E10 Approximation in the complex plane
41A10 Approximation by polynomials
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