On a Ahlfors-Denjoy Type Result
DOI:
https://doi.org/10.26713/cma.v5i1.230Keywords:
Ahlfors-Denjoy's Theorem, Asymptotic elements, Power series, Banach algebras, Power series' orderAbstract
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.Downloads
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.




