Derived and integrated sets of simple sets of polynomials in two complex variables. (English) Zbl 0604.41007

Kumuyi, W. F.; Nassif, M.

J. Approximation Theory 47, 270-283 (1986).

Composite polynomials in several variables are always very useful mathematical objects of study. Various problems relating to the properties of the derived sets of simple basic sets of polynomials are treated here with particular emphasis on distinction between the single and two complex variables cases. A positive result is established for the relationship between the Cannon functions of simple sets of polynomials in two complex variables and those of the directly derived sets. Possible extensions of results on the effectiveness of integrated sets for the single-variable situation to that of two variables are also discussed. Two important theorems summarise the main results of the paper.

Reviewer: P.Achuthan

MSC:

41A10

Approximation by polynomials

Keywords:

Composite polynomials; Cannon functions; effectiveness of integrated sets

References:

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