Effectiveness of Cannon and composite set of polynomials of two complex variables in Faber regions
Keywords:Basic set, Faber polynomials, Faber regions, Faber curves, Composite set, Cannon set, Cannon function, Cannon sum, Constituent set, Effectiveness
AbstractConditions 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.
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 Se?ries de base de polyno?mes quelconques. Paris: Gauthier-Villars, 1949.
How to Cite
Copyright (c) 2020 Jerome Ajayi Adepoju, Adesanmi Alao Mogbademu
This work is licensed under a Creative Commons Attribution 4.0 International License.