Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-03-0040

Keywords:

Basic set, Faber polynomials, Faber regions, Faber curves, Composite set, Cannon set, Cannon function, Cannon sum, Constituent set, Effectiveness

Abstract

Conditions are obtained for effectiveness of Cannon and Composite sets of polynomials of two complex variables in Faber regions. It generalizes to these regions the results of Nassif on composite sets in balls of centre origin whose constituents are also cannon sets.

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Author Biographies

  • Jerome Ajayi Adepoju, University of Lagos.

    Department of Mathematics.

  • Adesanmi Alao Mogbademu, University of Lagos.

    Department of Mathematics, Research Group in Mathematics and Applications.

References

J. A. Adepoju, “On effectiveness of basic sets of two complex variables in Polycylinders”, Complex analysis and applications, vol. 85, pp. 5-13, 1986.

A. I. Breadze, “The representation of analytic functions of several complex variables in Faber regions”, Sakharthveles SSR Mecmeretalhe Akademas Moambe, vol. 53, pp. 533-536, 1969.

M. Nassif, “Composite sets of polynomials of several complex variables”, Publicationes mathematicae Debrecen, vol. 18, pp. 43-52, 1971.

W. F. Newns, “On the representation of analytic functions by infinite series”, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 245, no. 900, pp. 429–468, Feb. 1953, doi: 10.1098/rsta.1953.0003

J. L. Ullman, “Studies in Faber polynomials. I”, Transactions of the American Mathematical Society, vol. 94, no. 3, pp. 515–515, Mar. 1960, doi: 10.1090/S0002-9947-1960-0112955-2

J. M. Whittaker and C. Gattegno, Sur les Séries de base de polynômes quelconques. Paris: Gauthier-Villars, 1949.

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Published

2020-06-03

Issue

Vol. 39 No. 3 (2020)

Section

Artículos

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Copyright (c) 2020 Jerome Ajayi Adepoju, Adesanmi Alao Mogbademu

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How to Cite

[1]
“Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions”, Proyecciones (Antofagasta, On line), vol. 39, no. 3, pp. 651–662, Jun. 2020, doi: 10.22199/issn.0717-6279-2020-03-0040.