On a Ahlfors-Denjoy Type Result

Authors

  • Roberto Contreras J. Edificio 104D, Ciudad Universitaria, Jardines de San Manuel, Puebla
  • Arnoldo Bezanilla L. Edificio 109C, Ciudad Universitaria, Jardines de San Manuel, Puebla

DOI:

https://doi.org/10.26713/cma.v5i1.230

Keywords:

Ahlfors-Denjoy's Theorem, Asymptotic elements, Power series, Banach algebras, Power series' order

Abstract

The present paper is concerned with the general problem of extending the classical theory of analytic functions of a Complex variable. The asymptotic behavior of power series defined on a Banach algebra with multiplicative functional or with a Gelfand theory is analyzed here and some lower estimates for the order of power series defined on this Banach algebras are given here.

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Author Biography

Roberto Contreras J., Edificio 104D, Ciudad Universitaria, Jardines de San Manuel, Puebla

Department of Applied and Basic Math. Faculty of Computer Science/Research Professor

References

A. Bezanilla López, Elementos Asintóticos de Funciones L-enteras sobre ílgebras de Banach Conmutativas y Acotaciones Inferiores para el Orden de la Función. Revista Ciencias Matemáticas XII (1) (1991), 35–46.

A. Bezanilla López, Sobre el Comportamiento Asintótico y el orden de Series de Potencias convergentes en un ílgebra de Banach. Revista Ciencias Matemáticas, Vol. XIII, No. 3, (1993), 17–30.

R. Choukri, El H. Illoussament and V. Runde, Gelfand Theory for non-commutative Banach algebras, Quarterly J. Math. Oxford 53 (2002), 161–172.

E.A. Gorin and C. Sánchez Fernández, Transcendental equations in commutative Banach algebras, Funct. Analysis and Appl. 11 (1) (1977), 63–64.

A.S.B. Holland, Introduction to the Theory of Entire Functions, Academic Press, New York, 1973.

E.R. Lorch, The theory of functions in normed Abelian vector rings, Transactions of The American Mathematical Society 54(3) (1943), 414–425.

A. SoÅ‚tysiak and C.K. Fong, Existence of a multiplicative functional and joint spectra, Studia Mathematica, T. LXXXI (1985), 213–220.

T.E. Angus and L.C. David. Introduction to Functional Analysis, John Wiley & Sons, New York, 1979.

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Published

15-07-2014
CITATION

How to Cite

Contreras J., R., & Bezanilla L., A. (2014). On a Ahlfors-Denjoy Type Result. Communications in Mathematics and Applications, 5(1), 41–46. https://doi.org/10.26713/cma.v5i1.230

Issue

Vol. 5 No. 1 (2014)

Section

Research Article

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