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

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 |

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\textit{W. F. Kumuyi} and \textit{M. Nassif}, J. Approx. Theory 47, 270--283 (1986; Zbl 0604.41007)

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### References:

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[2] | Nassif, M, Composite sets of polynomials of several complex variables, Publ. math. debrecen, 18, 43-52, (1971) · Zbl 0247.32004 |

[3] | Newns, W.F, On the representation of analytic functions by infinite series, Philos. trans. roy. soc. London ser. A, 245, 429-468, (1953) · Zbl 0050.07702 |

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[5] | Whittaker, J.M, Sur LES séries de base de polynomes quelconques, (1949), Paris · Zbl 0038.22804 |

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