On the Phragmén-Lindelöf principle for entire power series on a Banach algebra

Authors

  • Roberto Contreras-Juárez Autonomous University of Puebla. Faculty of Computer Science
  • Carlos Palomino-Jiménez Autonomous University of Puebla. Faculty of Computer Science

DOI:

https://doi.org/10.26713/cma.v6i1.304

Keywords:

Banach algebra, Phragmen-Lindelöf principle, Power series

Abstract

Many authors have managed to successfully extend the classical theory  of analytic functions to functions deï¬ned on more abstract spaces (see for example [3, 8, 9]). The purpose of this paper is to provide a bit in this direction. In this paper an extension of the Phragmén-Lindelöf principles of the classical theory to the functions expressed as power series on a Banach algebra not necessarily commutative, of course, involving concepts such as harmonic and subharmonic, is introduced.

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Author Biographies

Roberto Contreras-Juárez, Autonomous University of Puebla. Faculty of Computer Science

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

Carlos Palomino-Jiménez, Autonomous University of Puebla. Faculty of Computer Science

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

References

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Bezanilla López, A. Sobreel Comportamiento As intóticoyelordende Seriesde Potencias convergentes en un ílgebra de Banach. Revista Ciencias Matemáticas, Vol. XIII, No. 3, (1993), 17–30.

Blum, E. K. A theory of analytic functions in Banach algebras. Trans. Amer. Soc 78(1955), 343–370.

Contreras J., R. and Bezanilla L., A. Maximum module principle for power series on a Banach algebra. Divulgaciones Matemáticas12,No.2 (2004), 155–160 (in Spanish).

Contreras J., R. and Bezanilla L., A. On a Ahlfors-Denjoy Type Result. Communications in Mathematics and Applications 5, No.1 (2014), 41–46.

Evgrafov, M. A. Analytic functions. Dover Publications, Inc. New York, 1966.

Hille, E. and Phillips, R. S. Functional analysis ans semi-groups. Amer. Math. Soc., Colloquium Publications31, 1957.

Lorch, Edgar R. The Theory of Functions in Normed Abelian Vector Rings. Transactions of The American Mathematical Society 54(3), (1943), 414–425.

Mibu, Y. On the theory of regular functions in Banach algebras. Momors. of the College of Science, University of Kioto, Series A, Vol.XXXIII, MathNo.2, (1960), 323–340.

Hayman, W. K. and Kennedy, P. B. Subharmonic functions. Academic Press, Inc. New York,31, 1976.

Levin. B. Ya. Letures on entire functions. Translations of Mathematical Monographs, Vol. 150, 1991.

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Published

27-08-2015
CITATION

How to Cite

Contreras-Juárez, R., & Palomino-Jiménez, C. (2015). On the Phragmén-Lindelöf principle for entire power series on a Banach algebra. Communications in Mathematics and Applications, 6(1), 21–31. https://doi.org/10.26713/cma.v6i1.304

Issue

Vol. 6 No. 1 (2015)

Section

Research Article

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