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

Roberto Contreras-Juárez, Carlos Palomino-Jiménez


Many authors have managed to successfully extend the classical theory  of analytic functions to functions defined 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.


Banach algebra; Phragmen-Lindelöf principle; Power series

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